text:
Tag: Kim Stanley Robinson
This week we continued our exploration of the US postwar suburbs (see week 13), reading Ray Bradbury's Fahrenheit 451 (1953) and watching Invasion of the Bodysnatchers (Siegel 1956). Both texts were framed in relation to the period's culture of affluence and anxiety.
But first we began by placing Bradbury's novel in relation to genre – specifically the interweaving traditions of utopia/anti-utopia, utopia/dystopia and US magazine sf.
Thomas More coined 'Utopia' 500 years ago this year. When spoken aloud, the first syllable is a Latin pun on ou which means no and eu which means good (and topos means place) – so utopia means 'no place' but also suggests 'good place'. Utopia has come to be understood as a description of an imaginary world organised according to a better principle than our own, and to frequently involve not-always-gripping systematic descriptions of economic, social and technical arrangements. We discussed the efflorescence of utopian fiction in the wake of Edward Bellamy's Looking Backward, 2000-1887 (1888), and mentioned such key utopian authors as William Morris, Charlotte Perkins Gilman, Ursula Le Guin and Kim Stanley Robinson. We also noted the relative scarcity of utopian worlds in cinema – Just Imagine (Butler 1930), Things to Come (Menzies 1936) and Star Trek: The Motion Picture (Wise 1979) being potential examples, but all of them also demonstrating potentially negative elements and being susceptible to against-the-grain readings.
This led us to anti-utopias – texts that are in more or less explicit dialogue with someone else's utopian vision, exposing its darker, oppressive elements. William Gibson's 'The Gernsback Continuum', which we read last semester, is a kind of compendium anti-utopia, while novels such as Yevgeny Zamyatin's We (1924), Aldous Huxley's Brave New World (1932) and George Orwell's Nineteen Eighty-four (1949) are – among other things – direct responses to the utopian vision of HG Wells, drawing out its more totalitarian elements, as does Metropolis (Lang 1927).
During the 20th century, however, the explicit anti-utopia has given way to the proliferation of dystopias (dys + topia = bad place), dark, often satirical exaggerations of the worst aspects of our world. The dystopia emphasises bad aspects of our own world so as to make them more obvious (in this, they parallel the suburban world of All That Heaven Allows). The dystopia is not an explicit critique of the utopia, but a depiction of a world worse than our own – usually totalitarian, bureaucratic, brutal, dehumanising, and sometimes post-apocalyptic. Between us, we concocted a list of novels and films, including:
Kurt Vonnegut, Player Piano (1952)
Frederik Pohl and Cyril Kornbluth, The Space Merchants (1953)
John Wyndham, The Chrysalids (1955)
Anthony Burgess, A Clockwork Orange (1962), filmed as Clockwork Orange (Kubrick 1971)
Philip K. Dick, Do Androids Dream of Electric Sheep? (1968) filmed as Blade Runner (Scott 1982)
Harry Harrison, Make Room! Make Room! (1966), filmed as Soylent Green (Fleischer 1973)
Punishment Park (Watkins 1971)
THX 1138 (Lucas 1971)
Rollerball (Jewison 1975)
Mad Max (Miller 1979)
William Gibson, Neuromancer (1984)
Brazil (Gilliam 1985)
Margaret Atwood, The Handmaid's Tale (1985), film (Schlöndorff 1990)
Alan Moore and David Lloyd, V for Vendetta (1988–9), film: (McTeigue 2006)
Robocop (Verhoeven 1987)
PD James, The Children of Men (1992), filmed: (Cuarón 2006)
Octavia Butler, The Parable of the Sower (1993)
Kazuo Ishiguro, Never Let Me Go (2005), filmed: (Romanek 2010)
Gamer (Neveldine+Taylor 2009)
Moon (Jones 2009)
Suzanne Collins, The Hunger Games novels (2008-2010), filmed: Ross and Lawrence 2012-15)
Dredd (Travis 2012), based on Judge Dredd strip (1979–)
Elysium (Blomkamp 2013)
The widespread usage of dystopia and the relative decline of the utopia/anti-utopia tradition has led to an increased use of the eutopia (a term which makes linguistic sense as the opposite of dystopia) to describe imagined worlds that in some ways are better than ours, if still far from perfect. The eutopia imagines a better world, using its differences to indicate the shortcomings of our own world.
Both eutopia and dystopia are, in different ways, about the possibility of change.
We then turned to consider Ray Bradbury in the context of American sf in the 1950s. From the late 1930s, American magazine sf had been dominated by Astounding, edited by John W. Campbell. It was not the best-paying venue, but thanks to the galvanising effect Campbell – and his key authors, such as Robert A Heinlein and Isaac Asimov – had had on the field, it was the most respected and prestigious. That situation began to change after the war, particularly with the launch of The Magazine of Fantasy and Science Fiction and Galaxy, both of which could be characterised as being more literary, as being more interested such things as characterisation, atmosphere, slicker prose and satirical humour. Bradbury could not sell to Campbell, but published in wide range of sf magazines as well as in prestigious non-genre venues, such as Argosy and The Saturday Evening Post.
The reason for his failure with Campbell and success elsewhere has been attributed – by Brian Aldiss? – to him writing science fiction for people who don't like science fiction (which we might more generously describe as writing non-Campbellian science fiction). Bradbury was championed by critics such as Robert Conquest and Kingsley Amis who, although they occasionally wrote and edited sf, were not sf writers per se. Within the genre community, such writers/editors/critics as James Blish and Damon Knight tended to be more ambivalent – caught between what they saw as Bradbury' 'poetic' writing/ higher literary standards and his apparently blissful ignorance of science.
This ambivalence was mirrored by a number of the class, who found aspects of the novel quite compelling while also being frustrated by the 'vagueness' of its world-building. (I am not sure 'vagueness' is quite the right term, since it implies there is something that Bradbury should be doing rather than thinking about his preference for imagery over concrete images – and it might also indicate a relative lack of familiarity with sf's specific reading protocols, which often require the reader to collaborate in building the world from the smallest of hints.)
In considering Fahrenheit 451 as an exaggerated dystopian version of the suburbs it is perhaps useful briefly to put aside its most obvious and striking feature – firemen now burn books – and instead think about the other features of its imagined world, all of which resonate strongly with the affluence and anxieties outlined last week:
the overwhelming impact of mass media, on everything from the design of houses (no front porches, replace windows with TV screens, etc) to the fabric of domestic life, which is organised around consumption and pseudo-participation, and dominates social occasions
the alienation from other human beings, from nature, from meaningful labour
the reliance on tranquillisers, sleeping and other medication
the frequency of divorces and the virtual exile of children
women's rejection of pregnancy and natural childbirth (cast as a negative, although Shulamith Firestone and others would see this as a positive)
juvenile delinquents racing cars around night-time streets, dying in crashes and aiming for pedestrians
how commonplace deliberate suicides and accidental overdoses have become
the absence of an urban centre (there is one, but the emphasis throughout is on seemingly endless suburbs)
really long billboards because everyone drives so fast
the degradation of language
the constant sound of military jets and the ultimate outbreak of the fourth nuclear war since the 1960s
the near-universal and – it is made clear – willing abandonment of books and reading
the only very occasional spectacle of state power when books are burned
We also thought about the ways in which Bradbury's prose and imagery are 'simple' or 'child-like' – the way the novel seems to be the product of a pre-pubertal imagination. This led us in two directions.
First, there are the distinctly Oedipal elements of the novel. While its depiction of women is broadly misogynistic, this is especially focused on Mildred Montag. Cast as a simple-minded and anxious nag, she also comes across as a cold and distant mother figure to her husband, who often seems like a boy in quest of a father figure (Granger replacing Faber replacing Beatty). Mildred is early on associated with the kind of marble figure you might find on a mausoleum – remember the suburban fireplace in All that Heaven Allows – and when Montag turns the flamethrower on their twin beds (after all, there is no reason for mummy and daddy to share a bed, is there?), they 'went up in a great simmering whisper, with more heat and passion and light than he would have supposed them to contain' (151).
There is also something just a little bit queer about Montag's relationship with Faber, the older, educated man who first picked Montag up in a public park, slipping him his phone number even though he knew it would put him in the fireman's power. Faber maintains this role of mentor, and shares a strange intimacy with the Montag through the earbug the younger man wears so they can always be together.
The second direction in which this sense of Bradbury's simplicity went was thinking about the imagery he uses. The opening page introduces, among other images, the series of oppositions between black and white: firemen are always associated with blackness, and sometimes Bradbury seems almost to recognise a racial dimension; readers and women are associated with whiteness, although sometimes this whiteness is sepulchral (Mildred) or diseased (Faber). There is also animal and other nature imagery. Sparks become fireflies, books become pigeons. Later, books will rain down around Montag like pigeons, and he will be infected, losing control over his impulses, his hands becoming like ferrets whose antics he can only observe (this sense of alienation from his self culminates in him watching his own pursuit on television, which ends with his capture being faked). As with the bizarre fantasy about the barn in the final section of the novel, there is a nostalgic current underpinning the animal imagery – making manifest the natural world that the suburban sprawl roots up, tears down, eradicates. The imagery haunts the denatured suburb, reminding us of what has been lost and is constantly being thrown away.
Invasion of the Bodysnatchers shares many of these concerns. While its mood of paranoia might lend credence to the commonplace notion that the film is somehow about fears of communist infiltration, there is in fact little in the film to support reading it that way (just a few years earlier the emotionless nature of the pods would have been projected onto Nazis rather than Commies, primarily as a denial of the profound conformism in American life and in a consumer culture). Similarly, it is not especially easy to read the film as being about fears of racial passing or queer passing, although they too might be argued – the film is certainly about ensuring difference does not intrude onto this white suburban small town. This difference takes the form of two childless, sexually active recent divorcees – former sweethearts and possibly lovers – finding themselves thrown together, and everyone around them assuming they will become involved with each other again (while elsewhere, Oedipal anxieties take the form of children thinking there parents are not their parents). It is a film obsessed with sex – Miles makes constant innuendoes and hits on women all the time; he races over to Becky's house in his pyjamas (don't ask what her house is doing in his pyjamas) in the middle of the night and sweeps her off to his house, where the next morning she is wearing some of his clothes and cooking him breakfast, and Jack Belicec seems to assume this is post-coital. There is Becky's summer dress, which miraculously stays up while emphasising her breasts, and Miles's ultimate declaration that he did not know the real meaning of fear until he kissed her. Against all this sex is cast not only the asexual reproduction of the pod people but also the mechanical reproduction of commodities and the replacement of culture (a live band) by its simulacrum (the juke box).
And, as that penultimate hurried paragraph suggests, we ran out of time. Next week, Alphaville (Godard 1965).
AlSayyas, Nezar. Cinematic Urbanism: A History of the Modern from Reel to Real. London: Routledge, 2006. See chapter 9, "Exurban Postmodernity: Utopia, Simulacra and Hyper-reality."
Biskind, Peter. Seeing is Believing How Hollywood Taught Us to Stop Worrying and Love the Bomb. London: Pluto, 1983. 102–59.
Bould, Mark. "Burning Too: Consuming Fahrenheit 451." Literature and the Visual Media. Ed. David Seed. Woodbridge: DS Brewer, 2005. 96–122.
Grant, Barry Keith. Invasion of the Bodysnatchers. London: BFI, 2010.
McGiveron, Rafeeq O. "'To build a mirror factory': The Mirror and Self-Examination in Ray Bradbury's Fahrenheit 451." Critique: Studies in Contemporary Fiction 39.3 (1998): 282–7.
Seed, David. American Science Fiction and the Cold War: Literature and Film. Edinburgh: Edinburgh University Press, 1999.
–. "The Flight from the Good Life: Fahrenheit 451 in the Context of Postwar American Dystopias." Journal of American Studies 28.2 (1994): 22–40.
Whalen, Tom. "The Consequences of Passivity: Re-evaluating Truffaut's Fahrenheit 451." Literature/Film Quarterly 35.3 (2007): 181–90.
E.M. Forster's "The Machine Stops" (1909) anticipates surburban consumerist isolation.
Suburbia became a regular setting for postwar sf: Ray Bradbury's "There Will Come Soft Rains" (1950) and "The Pedestrian" (1951), Judith Merril's Shadow on the Hearth (1950), Frederik Pohl's "The Midas Plague" (1954), Philip K. Dick's Time Out of Joint (1959) and Pamela Zoline's "Heat Death of the Universe" (1967).
Examples of suburban horror include Anne Rivers Siddons's The House Next Door (1978) and M. John Harrison's subtler "The Incalling" (1978) and The Course of the Heart (1991).
Bradbury's novel was filmed by French New Wave director François Truffaut as Fahrenheit 451 (1966). Other sf and fantasy films depicting the dissatisfactions of suburban living include Invaders from Mars (Menzies 1953), Forbidden Planet (Wilcox 1956), The Stepford Wives (Forbes 1975), E.T. – The Extra-terrestrial (Spielberg 1982), Poltergeist (Hooper 1982), Parents (Balaban 1989), Edward Scissorhands (Burton 1990), Pleasantville (Ross 1998), The Truman Show (Weir 1998) and Donnie Darko (Kelly 2001).
Posted on February 5, 2016 February 8, 2016 Categories Books, Film, Horror, Monsters, Sf, The City in Fiction and FilmTags alan moore, aldous huxley, Alfonso Cuarón, anne rivers siddons, anthony burgess, bob balaban, Brian Aldiss, bryan forbes, charlotte perkins gilman, cyril kornbluth, damon knight, David Butler, david lloyd, david seed, don siegel, Duncan Jones, edward bellamy, em forster, Frances Lawrence, francois truffaut, Fred M. Wilcox, frederik pohl, fritz lang, gary ross, george lucas, George Miller, george orwell, Harry Harrison, isaac asimov, james blish, james mcteigue, jean-luc godard, John W. Campbell Jr, john wyndham, judith merril, kazuo ishiguro, Kim Stanley Robinson, kingsley amis, Kubrick, kurt vonnegut, m john harrison, margaret atwood, mark romanek, neill blomkamp, neveldine+taylor, norman jewison, Octavia Butler, pamela zoline, Paul Verhoeven, pd james, peter biskind, peter travis, peter watkins, peter weir, philip k dick, ray bradbury, richard fleischer, Richard Kelly, Ridley Scott, robert conquest, robert heinlein, robert wise, shulamith firestone, Spielberg, suzanne collins, Terry Gilliam, thomas more, tim burton, tobe hooper, ursula le guin, volker schlöndorff, william cameron menzies, william gibson, william morris, yevgeny zamyatinLeave a comment on The City in Fiction and Film, week 14
Le temps du loup aka Time of the Wolf (Michael Haneke France/Austria/Germany 2003)
[A version of this review appeared in Foundation 94 (2005): 134-137]
Although it has always produced outstanding sf and fantasy—from Jean Cocteau and Luis Buñuel to Andrei Tarkovsky and Jan Švankmajer—there was a time, back before I was born, when European arthouse cinema was synonymous with both cinematic and science-fictional excellence, when the nouvelle vague gave us Georges Franju's Les Yeux sans visage (1959), Chris Marker's La Jetée (1962), Alain Resnais's L'Année dernière à Marienbad (1961) and Je t'aime, je t'aime (1967), Jean-Luc Godard's Alphaville (1965) and Weekend (1967). This period is best captured not by Bernardo Bertolucci's joyless The Dreamers (2003) but, for all its gaucheness, Roman Coppola's CQ (2001), in which a young American filmmaker in Paris, desperate to be Godard, ends up completing a pop-camp sf movie even more heavily indebted to Mario Bava's Danger Diabolik (1968) than to Roger Vadim's Barbarella (1968), in which a sexy space-age spy must infiltrate the lunar base of Billy Zane's Che-like rebel leader.
Over the last couple of years, European arthouse directors have again been drawn to the fantastic and science-fictional. Thomas Vinterberg's It's All About Love (2003), Olivier Assayas's Demonlover (2002) and Michael Winterbottom's Code 46 (2004) attempt, with mixed success, to populate their Dickian/cyberpunk-flavoured tales with characters who at least vaguely resemble human beings. Vinterberg manages to produce several genuinely strange and estranging moments, but is undercut by a star-based narrative logic which forestalls complex intersubjectivity and opens the door to the worst kind of greetings card sentimentality; Assayas generates some sense of the perpetual displacement of the subject jetting through the spaces of global capital, but his film is no Pattern Recognition; and Winterbottom's impressive vision of the future which looks just like the contemporary Third World succumbs to the picturesque (and a really problematic rape scene in which Maria (Samantha Morton) literally asks for it). In Fear X (2002), Nicolas Winding Refn transforms a Wisconsin which already looked pretty alien—positively Canadian—into somewhere distinctly Lynchian, while Mathieu Kassovitz's Gothika (2003) occasionally rises above the ordinariness required of a Halle Berry vehicle. Although all of these films contain things to recommend them—some more than others—none of them measure up to those of forty years ago or, indeed, to Michael Haneke's Le temps du loup.
An immaculate MPV glides along a forest road. In it are Georges (Daniel Duval) and Anne (Isabelle Huppert) Laurent, their mid-teens daughter, Eva (Anaïs Demoustier), and her younger brother Ben (Lucas Biscome). Fleeing the city and some never-specified catastrophe, they have calmly made their way to their weekend house in the country; but a family of strangers have already moved in. When the agonisingly reasonable Georges offers them welcome and a share of their supplies, he is killed and Anne and the children are turned away. Despite knowing the Laurents, local villagers refuse them aid or shelter, and so they begin to wander the countryside, first joining up with an unnamed boy (Hakim Taleb) and then with a proto-community dominated by the petty tyranny of property-ownership and commerce—a set-up which does not survive the arrival of a larger group of refugees. Together, these displaced people await the arrival of a train which might take them to somewhere better.
It could be a trick of perspective, but the last few years seem to have produced a number of texts which return to the the kind of post-apocalyptic fiction once dismissed as cosy catastrophes (Wright's A Scientific Romance (1998), Lovegrove's Untied Kingdom (2003), Roberts's The Snow (2004), Robinson's Forty Signs of Rain (2004); the TV series The Last Train (1999); movies such as Reign of Fire (Bowman 2002), Twenty Eight Days Later (Boyle 2002), The Day After Tomorrow (Emmerich 2004) and Dawn of the Dead (Snyder 2004)), the best of which display at the very least an occasional flash of New Weird vigour, reinflating—with narrative and, occasionally, wit—a subgenre exhausted by the New Wave. What distinguishes Le temps du loup from them is a quite remorseless austerity, first signalled by the opening titles: small white uncluttered text on a black background, without music or sound. There are no CGI dragons. There are no zombies, enRaged or otherwise. There is no Big Weather. Indeed, it is difficult to reconcile the offscreen murder of Georges with the in-yer-face provocations and hi-jinks of Haneke's earlier home-invasion movie, Funny Games (1997).
In an accompanying interview, Haneke explains Le temps du loup's restraint in terms of not wanting to make a generic disaster movie but a film about personal relationships, of wanting to give the comfortable westerners used to watching the unfolding global catastrophe on TV a taste of what it would be like if it happened to them. In this he succeeds, but not necessarily in the way he intends.
The film relies on ellipses. The nature of the catastrophe is never explained (although livestock burning on a pyre in the background of one shot might provide a clue). We do not see Georges's death or his family having to bury him; we do not see their expulsion from their home or their theft of a bicycle; we do not see Ben's discovery of his dead budgerigar or a barn going up in flames; we do not see Anne's response to the letter Eva writes to her dead father, in which she talks about having to careful around her mother as she is on the verge of cracking up; and so on. Along with these omissions, there are also a number of scenes set in a pitch-black night, illuminated intermittently by the flame of a cigarette lighter or a handful of burning straw, and a number of unexplained events. This eschewal extends even to refusing emotional spectacle: when a sick child dies, there is a 30 second shot of hands fashioning a crude cross and placing it on the grave, followed by a two-and-a-half minute shot of the legs of the people gathered around the grave, the only sound being the mourning cries of the child's out-of-shot mother—and in the extreme distance, as the mourners move off, the flaming torches of an approaching group of refugees creep into shot, blurs of distant light in the falling dark.
The refusal to show does not extend to the characters; rather, all that the camera does is show us their stunned and stunted responses, and in this Haneke seems to be deliberately pursuing the kind of humanist-realism championed half a century ago by André Bazin. The camera's cool gaze stays resolutely outside of the characters, but frequent long takes provide the time to watch minute gestures and changes of expression and to ponder motivation and meaning. There is, for example, an aching moment when we can see Eva trying to choose between loyalty to a mother ill-equipped to handle the new situation and the teenage boy who has already learned to strip whatever he needs from corpses (and some time later, we see her growing realisation that the boy is differently, but equally, ill-equipped). In the same sequence, a close-up reveals the sorrowful wisdom of the even younger Ben who, unlike his family, knows there is no point running after a passing train, crying for help. This sense of externality counters Haneke's desire to focus on relationships, and perhaps only twice produces the kind of the effect on the viewer he seeks. First, and overwhelmingly, is the sense of disconnection: just as the family have no idea what has happened or what will happen next, so the film's omissions and ellipses makes the experience of the narrative an uncertain one; while it grips, the succession of incidents also produces a sense of being stunned, akin to that experienced by the characters. Second, the conclusion that Ben reaches, the sacrifice he decides to make to save his family, simultaneously comes out of the blue and is inevitable. It is a moment every bit as human and as terrible as the scene in Thomas Disch's 'The Asian Shore' about the young boy struggling to carrry two buckets of water whose shoes come off every time he takes a few steps; and the ground is freezing; and every time he puts his shoes back on he spills more of the water over himself; and he is freezing; and just as Disch's narrator cannot help because he cannot communicate with the boy, so we cannot save Ben from his decision even though we know it will not work and its cost is unimaginably high.
The low-budget Last Night (McKellar 1998), dubbed 'the Canadian Armageddon', stands out among the recent 'not-so-cosy' catastrophes, not least because it refuses the apocalypse a post-. Similarly, and like Weekend, to which its long tracking shots might pay homage, Le temps du loup is ultimately not about life after the apocalypse—the survivors are numb, powerless; there is no attempt to rebuild civilisation—but about life during the apocalypse going on around us, mostly unseen. Like Benjamin's angel of history (and, perhaps, Code 46), Haneke's film sees not progress but one single catastrophe which keeps piling wreckage upon wreckage. The closing shot, which lasts for over two minutes, is filmed, the soundtrack implies, from aboard a train as it races through a verdant French countryside. We do not see the train. We do not know whether it is the one for which the characters have been waiting or, if so, whether it stopped to pick them up. We do not even know whether it is real, or merely a fantasy like the one spoken of in the preceding scene ('maybe tomorrow, there'll be … a big car racing up. … And a guy will get out and say everything's fine again. And water will flow in our mouths with roast pigeons and maybe the dead will come back to life'). And while the final shot shows that the land, like the people whose story we've followed, endures, it is a land, perhaps significantly, deserted of people.
Posted on June 16, 2015 June 16, 2015 Categories Film, SfTags adam roberts, alain resnais, André Bazin, andrei tarkovsky, Bernardo Bertolucci, billy zane, che, chris marker, danny boyle, don mckellar, georges franju, halle berry, Isabelle Huppert, james lovegrove, Jan Švankmajer, Jean Cocteau, jean-luc godard, Kim Stanley Robinson, Luis Buñuel, mario bava, mathieu kassovitz, Michael Haneke, michael winterbottom, nicolas winding refn, olivier assayas, philip k dick, rob bowman, Roger Vadim, roland emmerich, Roman Coppola, ronald wright, samantha morton, thomas disch, thomas vinterberg, walter benjamin, william gibson, zack snyderLeave a comment on Le temps du loup aka Time of the Wolf (Michael Haneke France/Austria/Germany 2003)
Kim Stanley Robinson, The Years of Rice and Salt (London: HarperCollins, 2002)
[A version of this review originally appeared in Foundation 86 (2002), 134-36]
Bold Bardash, a Mongol horseman in the army of Temur the Lame, crosses through the Moravian Gate and onto the Magyar Plain, and there finds Europe dead, victim of a plague that has killed nearly everyone on the continent. Forced to flee Temur, he heads south to the Mediterranean, where he is captured and sold into slavery. As he sails east to China, he befriends the teenage Kyu, a fellow slave. Various adventures see them become members of the Yongle Emperor's household, travelling between Nanjing and Beijing. But things end badly, and a tenth of the way through the novel they are dead.
Reunited in bardo, the afterlife, they await rebirth. Bold, Kyu, I-li and several other characters are members of a karmic jati, and when they reincarnate, their lives will again intertwine.
The opening book, 'Awake to Emptiness', establishes the basic pattern for the following nine, each of which is written in a slightly different style. For example, 'Awake to Emptiness' imitates aspects of Wu Ch'êng-ên's The Journey to the West, with passages of incidental verse, and narrative hooks at the end of each chapter:
One of the sailors happily names it: 'Alexandria!' Bold had heard the name, though he knew nothing about it. Neither do we; but to find out more, you can read the next chapter (23)
whereas Book Six, 'Widow Kang', contains marginal commentary, a sometimes sarcastic scholarly exegesis of unfamiliar terminology which also hints at the meaning of the novel's title (372).
Each book is set in a different period of the seven hundred years following the death of Europe, producing an alternative history centred on Asia, but also including North Africa, colonised Europe, and a North America in which the native American Hodenosaunee League occupies the central region between Chinese invaders on the West Coast and Muslim invaders on the East Coast (one of the novel's tributes to Dick's The Man in the High Castle; there are also a couple of references to Tagomi-san). Later books trace the spread of Islam, the temporary establishment of an Islamic utopia, an attempted Chinese invasion of Japan, the discovery of the New World, a revolution in bardo, the birth of empirical science, the establishment of the Hodenosaunee League, attempts at religious co-existence, the industrialisation of warfare and a 70-year long world war, and the gradual development of a world-wide League based on mutual interdependence and responsibility.
Previously, Robinson has deployed various conceits to ensure continuity of viewpoint over a long historical span – such as the Mars trilogy's anti-agathic drugs, which extend the lives of key members of the First Hundred – or in alternative versions of the same world. In The Years of Rice and Salt, he achieves the latter by doing precisely what Clute suggests he did in the Orange County trilogy, using the same characters under new names (Clute and Nicholls, The Encyclopedia of Science Fiction 1015); and to assist the reader in following them through their multiple incarnations, he uses a naming device ascribed to 'the Samarqandi anthologist Old Red Ink' (649). However, as the novel progresses, reincarnation starts to be treated by the characters as a useful metaphor which needs to be reconceptualised in secular terms: humans live again through our children; when we are remembered or when, unremembered, we nonetheless affect the way people behave; when broken down into atoms, 'we are diffusely reincarnate throughout the universe' (664). Most importantly, reincarnation can be achieved by thinking of the species as the organism. It lives on, with history or language or DNA as its consciousness and, as Bao Xinhua says,
if we think of it that way, then it might increase feelings of solidarity and obligation to others. It makes it clearer that if there is a part of the body that is suffering, and if at the same time another part commandeers the mouth and laughs and proclaims that everything is really fine … then we understand more clearly that this creature-species or species-creature is insane, and cannot face its own sickness-unto-death. Seen in that sense, more people might understand that the organism must try to keep itself healthy throughout its whole body. (665)
Ultimately, The Years of Rice and Salt tells us not just that other worlds are possible, but that another world is possible.
One of the basic attractions of the alternative history for both reader and writer is the puzzle element: what was the initial moment of divergence from the historical record? For example, the pervasive anachronism in Gibson and Sterling's The Difference Engine is commonly said to stem from Babbage's success at transforming his designs for mechanical computers into working machines; but as this could not happen without advances in metals technology and engineering, the authors alter economic, social and political circumstances by positing a revolution in which a coalition of workers, scientists and capitalists overthrew the Duke of Wellington around 1830. Byron's leadership of this pro-industrial faction is in turn attributed to his wife's decision in 1815 to stay with him despite his peccadilloes. This event has typically been described as the point of divergence for The Difference Engine, yet there are hints of at least one earlier change to the historical record: the successful establishment by Wordsworth and Coleridge of the Pantisocracy, a utopian community, in North America (that was really proposed by Coleridge and Southey in the 1790s). Did their absence from the British literary scene mean that Romanticism failed to take hold, leading to political rather than poetical careers for both Byron and the Luddite leader, Shelley? Are there even earlier divergences?
This puzzle aspect of the alternative history points to the form's dependence on a shared epistemic base: we know that the Spanish Armada, the South and the Nazis did not win that vampires do not exist (Roberts's Pavane, Moore's Bring the Jubilee, Deighton's SS-GB, Stableford's The Empire of Fear, respectively), and, to take an example from Robinson, that America did drop an atom bomb on Hiroshima ('The Lucky Strike'). Alternative histories then work by establishing how the world created by the alteration differs from our own. This is the other aspect of the shared epistemic base: the reader must be familiar with the historical record that is being changed.
In The Years of Rice and Salt, Robinson offers a magnificent misprision of the form. He has created an intricate alternative history of cultures whose real-world history is largely excluded from Western mass education. This is a profoundly political act, and one which could not be more timely as ignorance of Islamic cultures forms the basis of the stereotyping which is used to justify slaughter of Afghan civilians, oppression of Palestinians and genocidal sanctions on Iraq. Throughout the novel Robinson draws multiple perspectives on the many strands of Islam and the variety of Chinese and Japanese cultures. Sometimes these cultures seem to match stereotypes all too common in the real world – Islam as viciously repressive, the Chinese as yellow peril – but Robinson's world is too vast and complex to allow these views to go unchallenged. For example, Islam is mourned as a religion with a more or less feminist and egalitarian core in the Quran that has been lost behind the hadith (later teachings which have rather more to do with the subjugation of the people and the maintenance of power); later, other muslims propose looking for what is most buddhist in their religion.
The structure of the novel enables Robinson to demonstrate once more his tremendous skill at novella-length writing, his marvellous economy in creating credible characters, his eye for many different landscapes, and his thematic complexity and coherence over both shorter and longer lengths. He remains a didactic writer, but the various discussions about politics and theories of history that appear throughout The Years and Rice of Salt are vital, integral and invigorating.
It is a work to be pondered, certainly, but more than that, to be savoured.
Posted on June 3, 2015 Categories Books, SfTags brian stableford, bruce sterling, john clute, keith roberts, Kim Stanley Robinson, len deighton, philip k dick, sf, ward moore, william gibson, Wu Ch'êng-ênLeave a comment on Kim Stanley Robinson, The Years of Rice and Salt (London: HarperCollins, 2002)
Best books of the millennium so far
The BBC asked a bunch of US critics, what is the greatest novel of the millennium so far? Such an obviously completely bullshit question, you can imagine my eagerness to see the results. I was really looking forward to the pleasure of being outraged and/or bemused by their idiocy and poor taste. That's the kind of thing that gets me through the day.
What can I say? I was robbed.
Junot Díaz's The Brief Wondrous Life of Oscar Wao topped the poll. And, leaving aside for one moment the obvious and complete bullshitness of the question, I had no problem with that. I like the novel an awful lot. And Junot very generously blurbed the Africa SF collection and contributed an extraordinary long interview to the SF Now collection, extracted here, so I'm very happy for him personally. But none of that helps when I'm jonesing for affront.
The situation was redeemed a little by one of the judges comparing Oscar Wao to Philip Roth's Portnoy and John Updike's Rabbit. What the fuck? At last some provocation! Such pedestrian taste! How benevolent of white literary culture to elevate Díaz to such company! The unsavoury reek of appropriation, not only of Dominican/Latino culture, but of geekdom, too! Who dared to say such a thing?
I clicked on the link, and was once more robbed. The journalist is paraphrasing Greg Barrios' interview with Díaz in the Los Angeles Review of Books, in which the comparison – which also mentions James T Farrell's Studs Lonigan – is really just an attempt to explain the structure of the series of Oscar Wao stories Díaz once contemplated writing.
Maybe the other 19 titles in the poll's top twenty would offer some enormity, some better shots at genuine WTF moments.
Of the other books, I have read only three.
Michael Chabon's The Amazing Adventures of Kavalier & Clay (number 6) has been sitting on the shelf for years. I finally overcame the potential embarrassment of being seen not to have read it yet, and got through it in one long sitting on two trains and two planes (serially, not simultaneously) en route to the US. A thoroughly enjoyable romp, full of geek-stroking moments, and I get why people like it so much. But all the way through I was troubled by how comfortable it was. How comforting to imagine twentieth-century American history so utterly free from any anti-Semitism whatsoever. It just seemed dishonest. Good, but a long way short of great. On the whole, I probably rate Jonathan Lethem's vaguely comparable Fortress of Solitude more highly. (By coincidence, my partner, sat next to me on one of the trains and both of the planes, read Hilary Mantell's Wolf Hall (number 3), and had a kind of mehhh response. Neither book made the return journey.)
A professional obligation recently required me to read Zadie Smith's NW (number 18). It took me completely by surprise. A genuinely compelling page-turner, if ultimately also just a bit too comfortable in its rather bourgeois worldview. I promptly bought White Teeth (number 11), but have not had chance to read it yet.
Cormac McCarthy's The Road (number 17) utterly mystifies me. It is flimsy and trite and I really cannot see what anyone sees in it. But people damn well keep on seeing something in it.
Three others are in the to-read pile or, rather, one of the to-read piles, 'cos this place is becoming unmanageable again. There is a looming happy convergence of personal interest and work which will hopefully get me to Edward P Jones's The Known World (number 2) and Chimamanda Ngozi Adichie's Half of a Yellow Sun and Americanah (numbers 10 and 13) within the next year.
Jeffrey Eugenides's Middlesex (number 12) has been flickering in and out of a similar indeterminate space for a few years now, but every time I decide this time I really do need to read it I realise I don't actually have a copy.
Roberto Bolaño's 2666 (number 19) would be in a to-read pile but I am determined to read one of these shorter books of his I have lying around before committing to such a sizeable tome. I mean, over there in the corner, there's a small mountain range comprised of the evergrowing proportion of William Vollmann that remains unread. Surely I should do something about that first?
I confess to finding the whole idea of Jonathan Franzen (The Corrections, number 5) baffling. At least he only provokes indifference.
But Ian McEwan? (Atonement at number 9). Genuine ire.
I have not managed to get past the first chapter of anything McEwan has written since, I dunno, Black Dogs or possibly Enduring Love, though I can recall nothing about either of them. (I remember quite liking The Cement Garden and The Comfort of Strangers, and the two early story collections, which is why I stuck with him as long as I did, but I was fifteen or sixteen when I read them, so I doubt it is worth going back.)
At least, I suppose, we are spared Martin Amis. I agreed wholeheartedly with Beulah Maud Devaney's statement this week that 'life is too short for Martin Amis', though found myself repeatedly moving her words and their meanings around a little. Martin Amis is too short to live! Let's shorten the life of Martin Amis!
Nothing on the rest of the list provoked a thing. Least of all interest.
I don't know which are the greatest novels of the millennium so far. Not least because is it such an obviously and completely bullshit idea. But here is my list of the books published so far this millennium that I rate most highly. My criteria boil down to this: I could not wait to finish them so I could force my copies on other people to read. Which is unusual for me since, despite my enthusiasms, I am not by nature enthusiastic.
In date order:
Kim Stanley Robinson, The Years of Rice and Salt
Ahmadou Kourouma, Waiting for the Wild Beasts to Vote (this is cheating a little, since it was published in France in 1998)
Nalo Hopkinson, The Salt Roads
Neal Stephenson, The Baroque Cycle
Gwyneth Jones, Life – I also rate her Rock and Roll Reich series (2001-14) very highly; it is becoming increasingly prescient.
Geoff Ryman, Air: Or, Have Not Have
Shelley Jackson, Half Life
Anthony Joseph, The African Origins of UFOs
Thomas Pynchon, Against the Day
Ngũgĩ wa Thiong'o, Wizard of the Crow
Junot Díaz, The Brief Wondrous Life of Oscar Wao
Hari Kunzru, My Revolutions
China Mieville, The City & the City – or perhaps Iron Council (2004), actually, the whole Bas Lag trilogy (Perdido Street Station, The Scar)
Nnedi Okorofor, Who Fears Death
Karen Tei Yamashita, I Hotel
Andrea Hairston, Redwood and Wildfire
John Sayles, A Moment in the Sun
Zadie Smith, NW
Posted on January 24, 2015 June 12, 2015 Categories Books, SfTags Ahmadou Kourouma, Andrea Hairston, Anthony Joseph, Chimamanda Ngozi Adichie, China Mieville, Geoff Ryman, Gwyneth Jones, Hari Kunzru, Ian McEwan, John Sayles, Jonathan Lethem, Junot Diaz, Karen Tei Yamashita, Kim Stanley Robinson, Martin Amis, Michael Chabon, Nalo Hopkinson, Neal Stephenson, Ngugi wa Thiong'o, Nnedi Okorofor, Roberto Bolano, Shelley Jackson, Thomas Pynchon, Zadie SmithLeave a comment on Best books of the millennium so far


text:
Brown Recluse Spider Toxicity
Ifeanyichukwu Anoka
Erika Robb
Mari Baker
Sebastiano Cassaro
Tanya Egodage
In the United States, Loxosceles reclusa or brown recluse spiders are found mostly in the south, west, and midwest areas. They are usually in dark areas such as under rocks, in the bark of dead trees, attics, basements, cupboards, drawers, boxes, bedsheets, or similar locations. Dermonecrotic arachnidism is the local tissue injury that results from brown recluse spider envenomation, while loxoscelism describes the systemic syndrome caused by envenomation.[1]
In the USA, the venom of the Loxosceles reclusa is the most potent among arachnids and most likely to cause dermonecrotic arachnidism.[2]
Systemic involvement, while rare, is more likely to occur in children than in adults. There has recently been an increase in reports of brown recluse spider bites even in nonendemic areas. Most of these reports are likely because of other causes of similar appearing skin lesions like methicillin-resistant staph aureus skin infections.[3]
Brown recluse spider venom is cytotoxic and hemolytic. It has many enzymes that contribute to the clinical manifestations. Sphingomyelinase D, one of the more well-studied components, has been shown to direct toxin-mediated hemolysis and complement-mediated erythrocyte destruction. It does this by activating the complement system. Within the venom, there are additional proteases that degrade collagen, fibronectin, fibrinogen, gelatin, elastin basement membranes that on their own may not be able to cause the local reaction seen with brown recluse bites but seem to have a synergistic effect with sphingomyelinase D leading to many of the cutaneous findings. Hyaluronidase, alkaline phosphatase, esterase, and ATPase also seem to have effects leading to the cutaneous manifestations of bites.[4]
To further study the necrotic effects of the brown recluse spider bite, there was a study done with rabbits injected with the venom. Although a small sample size, findings showed inflammatory infiltrates, coagulative necrosis and vasculitis. With all samples, there was a zone of eosinophils referred to as "mummified" coagulative necrosis seen between the epidermal and dermal layers.[5]
Brown recluse spider bites usually occur while indoors and as a defense mechanism as they are crushed or rolled over in bed. Some bites will present with only an urticarial rash. If the bite is more severe, the course usually is as follows. The initial bite will be painless, but over the subsequent two to eight hours it will become increasingly painful. Systemic symptoms of brown recluse venom can present as malaise, nausea, headache, and myalgias. In children, the systemic reaction is more severe and may also include weakness, fever, joint pain, hemolytic anemia, thrombocytopenia, organ failure, disseminated intravascular coagulation, seizures, and death.
The bite site may initially have two small puncture wounds with surrounding erythema. From there, the center of the bite will become paler as the outer edge becomes red and edematous; this relates to vasospasm which will cause the pain to become more severe. Over the next few days, a blister will form, and the center of the ulcer will turn a blue/violet color with a hard, stellate, sunken center. After this step, skin sloughing can occur, and the wound will eventually heal by secondary intention, but this can take several weeks.
The bite of a brown recluse spider bite is a clinical diagnosis. A diagnosis of a spider bite can be made definitively only if the patient has a lesion that is consistent with a spider bite, or the spider was seen biting the patient, and the spider is caught and identified by an entomologist.
If the clinician makes a working diagnosis of a brown recluse spider bite, lab testing is unnecessary except if there are systemic complaints, especially in children.[6] In these patients the following laboratory studies are performed;
Serum calcium and phosphate
CK/myoglobin
PT/ INR
D Dimer
Often a bite from a presumed arachnid can be mistaken as a bite from the brown recluse spider. Most patients aren't able to find the spider. A helpful mnemonic to use is NOT RECLUSE,[7] to help exclude the cause of bite from a brown recluse spider.
N (numerous) - only one lesion is usually present in a brown recluse spider bite.
O (occurrence) - A bite usually occurs when disturbing the spider. As the name suggests, they tend to avoid people, hiding in dark spaces like in a box or the attic.
T (timing) - Most bites occur between April and October.
R (red center) - characteristic bites will have a pale central area secondary to the capillary bed destruction causing ischemia.
E (elevated) - Usually the bites are flat. If the area is elevated >1 cm, then this is most likely not a brown recluse spider bite.
C (chronic)- bites from a brown recluse spider most commonly heal within 3 months.
L (large) - Rarely are these bites >10 cm.
U (Ulcerates too early) - If the bite is from a brown recluse spider, they do not ulcerate until 7-14 days.
S (swollen) - often brown recluse spider bites do not exhibit significant swelling unless they occur on the face or the feet
E (exudative) - brown recluse spider bites do not cause exudative lesions
Initial treatment should begin with simple first aid. Elevate the extremity above the heart or at least in a neutral position. The activity of sphingomyelinase D is temperature dependent so an ice pack to the area should help halt the necrosis process.[8] Clean the wound with soap and water and ensure the patient's tetanus immunization is up to date. NSAIDs can provide pain management, but some people may need opioids. Antibiotics are only necessary if there is associated cellulitis.
There is scant evidence for the use of dapsone or antivenom.[9] Also, note that dapsone is harmful in patients with G6PD deficiency,[10] and can also cause deadly hypersensitivity reactions.[11] Steroids may be beneficial as they have been shown to decrease hemolysis and help prevent renal failure. If the infection is severe, consider hyperbaric oxygen therapy and surgical excision after the wound is well demarcated may be a consideration.[2] Early surgical debridement is not advisable.
Management for systemic symptoms is different than for local effects; hospital admission is the recommendation for patients with hemolytic anemia, rhabdomyolysis, disseminated intravascular coagulation or end-stage organ failure. Treatment of these conditions is not different in this scenario than it would be for any other cause.
In children, systemic loxoscelism may preclude skin findings and should be considered as a differential in pediatric patients with undifferentiated acute hemolytic anemia especially in regions known to have the brown recluse spider. Hemolysis has been reported up to 7 days after spider bite so adequate follow up instructions should be given to parents of children even if there are no systemic findings during the ED visit.[12] At a minimum, one should obtain a urinalysis at the initial visit if the working diagnosis is a brown recluse spider bite and the patient is being discharged.
MRSA skin infections
Deep fungal infections
Cutaneous anthrax
Pyoderma gangrenosum
Other insect bites
Most cases of Brown recluse Spider envenomation manifest only as local soft tissue destruction. Death is rare but has been reported especially in children.[13][14]
After 4 to 6 weeks of therapy, it may be necessary to proceed with delayed skin grafting.
Most spider bites are harmless. Death from brown recluse spider bites are rare and have been reported only in children.
Identifiable Features: The brown recluse spider may be identifiable by the violin pattern on the cephalothorax which attaches to the legs, although other species may exhibit similar markings.
Habits; Most bites occur in the summer months. The spiders like to hide in warm, dark corners and crevices like attics, garages, shoes, bed corners. The spiders are usually not aggressive and bite as a defense mechanism when they are being pressed against a surface by the skin of the patient.
Venom; The brown recluse spider venom is very poisonous but rarely causes a lot of damage because of the small quantity. One of the active enzymes in the venom causes significant damage to blood vessels and cell death to the tissue at the envenomation site. Also, the venom causes the patient's body to release inflammatory cells like interleukins, cytokines to help deal with the venom but these cells can cause harm to the patient once they activated; this results in red blood cell destruction (hemolysis), platelet destruction (thrombocytopenia), end-organ damage (kidney injury and coma).
Symptoms; Bites are usually painless initially; patients will start to feel a stinging sensation after about 3 hours. Look out for redness around the site and fang marks. Most commonly, there will be a white blister formation that progresses to scarring and healing over a few weeks. Less commonly, one will see blue discoloration after the blister formation that progresses to necrosis and an ulcer formation. Patients may also experience nausea, vomiting, severe itching, and muscle pain.
Diagnosis: In the event of a spider bite, the best course is to see a doctor on the same day. If possible, bring the spider as this will help with a definitive diagnosis. Lab tests are not necessary if the patient only has skin complaints but if thee are systemic complaints like fever, headache, muscle pain the doctor may order a complete blood count, electrolyte panel, check coagulation studies, kidney function and urinalysis.
Treatment: Before presenting to the ED, the following are steps to take:
Clean the bite site with soap and water
Elevate the area above the level of the heart
Apply ice to the area
Treat pain with acetaminophen
Additional treatment options include; tetanus immunization, antihistamines for itching, antibiotics if there are signs of infection, escalation of pain medications. There are no antivenoms available in the US. Some have suggested dapsone and systemic steroids, but there is little to no evidence they work, and these medications can have serious side effects.
Daily follow up with a primary care physician to determine the extent of skin damage
Admission for observation and further care if there are systemic findings and or lab abnormalities
If there is skin necrosis, the patient will eventually need to be evaluated by a surgeon
Brown recluse spider bites typically only cause cutaneous findings that are localized but sometimes can progress to systemic injury and, rarely, death. Most of these patients will present to the emergency department where they will encounter an ER nurse and emergency medicine physician or physician assistant. The ER nurse will assist with lab draws and local wound care. If admission to the hospital is deemed unnecessary, the patient will need to be seen by their primary care physician over the next few days to monitor the wound progression. If there is an ulcer formation, the patient will eventually need to be evaluated by a general surgeon. If the patient develops systemic findings or lab abnormalities, it would be prudent to involve the toxicologist in the patient's care to render their recommendations. In the event of end-organ damage like acute kidney injury, a nephrologist will need to be involved in the patient's care.
Contributed by Wikimedia Commons (Public Domain)
Attributed To: Contributed by Wikimedia Commons (Public Domain)
Brown Recluse Spider Toxicity - Questions
A patient was cleaning out her garage earlier this morning noticed a burning, white blister with surrounding erythema on the dorsum of her foot about 5 hours later. The patient also complains of a headache, muscle pain, fever. What orders should be obtained by the physician?
(Move Mouse on Image to Enlarge)
CBC, CMP, UA, CK, Myoglobin, PT ,INR , D Dimer
Foot Xray, CT head, EKG
MRI Brain, blood cultures, Lumbar Puncture
A patient presents with a skin lesion, she thinks she was bitten by a brown recluse spider. How should one make a definitive diagnosis?
Contributed by Creative Commons, (CC BY 2.0) https://creativecommons.org/licenses/by/2.0/deed.en
Attributed To: Contributed by Creative Commons, (CC BY 2.0) https://creativecommons.org/licenses/by/2.0/deed.en
Characteristic skin lesion plus the spider being observed inflicting the bite and the spider was recovered and identified by an expert
A characteristic skin lesion alone
A characteristic skin lesion plus fever
A characteristic skin lesion plus myalgia
A patient was cleaning out her garage earlier this morning noticed a burning, white blister with surrounding erythema on the dorsum of her foot about 5 hours later. What insect envenomation is associated with the described reaction?
A previously healthy 6-year-old female is brought to the clinic for evaluation for signs and symptoms developing following a spider bite. 2 days ago, the child was getting toys out of the closet when a brown spider bit her on the left arm. Since then the area of the bite has become dark in color, and today the child began to complain of a headache, nausea and had one episode of vomiting. Vitals signs reveal pulse 120 bpm, blood pressure 100/68 mmHg, respiratory rate 24/minute and temperature 100.3 Fahrenheit. Exam of the arm demonstrates a 1.5 cm of dark central ecchymosis, which is surrounded by an area of pallor and an outside ring of erythema. What test(s) should be ordered to identify the serious complications associated with this bite?
Liver function tests and lipase
Serum calcium and creatine kinase (CK)
Serum lactate and procalcitonin
CBC and coagulation profile
Brown Recluse Spider Toxicity - References
NOT RECLUSE-A Mnemonic Device to Avoid False Diagnoses of Brown Recluse Spider Bites., Stoecker WV,Vetter RS,Dyer JA,, JAMA dermatology, 2017 May 1 [PubMed]
Histological findings after brown recluse spider envenomation., Elston DM,Eggers JS,Schmidt WE,Storrow AB,Doe RH,McGlasson D,Fischer JR,, The American Journal of dermatopathology, 2000 Jun [PubMed]
Chaves-Moreira D,Senff-Ribeiro A,Wille ACM,Gremski LH,Chaim OM,Veiga SS, Highlights in the knowledge of brown spider toxins. The journal of venomous animals and toxins including tropical diseases. 2017; [PubMed]
Hadanny A,Fishlev G,Bechor Y,Meir O,Efrati S, Nonhealing Wounds Caused by Brown Spider Bites: Application of Hyperbaric Oxygen Therapy. Advances in skin [PubMed]
Cohen PR, Community-acquired methicillin-resistant Staphylococcus aureus skin infections: a review of epidemiology, clinical features, management, and prevention. International journal of dermatology. 2007 Jan; [PubMed]
Manzoni-de-Almeida D,Squaiella-Baptistão CC,Lopes PH,van den Berg CW,Tambourgi DV, Loxosceles venom Sphingomyelinase D activates human blood leukocytes: Role of the complement system. Molecular immunology. 2018 Feb; [PubMed]
Bernstein B,Ehrlich F, Brown recluse spider bites. The Journal of emergency medicine. 1986; [PubMed]
Manríquez JJ,Silva S, [Cutaneous and visceral loxoscelism: a systematic review]. Revista chilena de infectologia : organo oficial de la Sociedad Chilena de Infectologia. 2009 Oct; [PubMed]
Merchant ML,Hinton JF,Geren CR, Sphingomyelinase D activity of brown recluse spider (Loxosceles reclusa) venom as studied by 31P-NMR: effects on the time-course of sphingomyelin hydrolysis. Toxicon : official journal of the International Society on Toxinology. 1998 Mar; [PubMed]
Belfield KD,Tichy EM, Review and drug therapy implications of glucose-6-phosphate dehydrogenase deficiency. American journal of health-system pharmacy : AJHP : official journal of the American Society of Health-System Pharmacists. 2018 Feb 1; [PubMed]
Shukkoor AA,Thangavelu S,George NE,Priya S, Dapsone Hypersensitivity Syndrome (Dhs): A Detrimental Effect Of Dapsone? A Case Report. Current drug safety. 2018 Jul 31; [PubMed]
Raza S,Shortridge JR,Kodali MK,Nistala P,Kale G,Doll DC, Severe haemolytic anaemia with erythrophagocytosis following the bite of a brown recluse spider. British journal of haematology. 2014 Oct; [PubMed]
Rosen JL,Dumitru JK,Langley EW,Meade Olivier CA, Emergency department death from systemic loxoscelism. Annals of emergency medicine. 2012 Oct; [PubMed]
Wright SW,Wrenn KD,Murray L,Seger D, Clinical presentation and outcome of brown recluse spider bite. Annals of emergency medicine. 1997 Jul; [PubMed]
The intent of StatPearls is to provide practice questions and explanations to assist you in identifying and resolving knowledge deficits. These questions and explanations are not intended to be a source of the knowledge base of all of medicine, nor is it intended to be a board or certification review of Surgery-General. The authors or editors do not warrant the information is complete or accurate. The reader is encouraged to verify each answer and explanation in several references. All drug indications and dosages should be verified before administration.
StatPearls offers the most comprehensive database of free multiple-choice questions with explanations and short review chapters ever developed. This system helps physicians, medical students, dentists, nurses, pharmacists, and allied health professionals identify education deficits and learn new concepts. StatPearls is not a board or certification review system for Surgery-General, it is a learning system that you can use to help improve your knowledge base of medicine for life-long learning. StatPearls will help you identify your weaknesses so that when you are ready to study for a board or certification exam in Surgery-General, you will already be prepared.
Our content is updated continuously through a multi-step peer review process that will help you be prepared and review for a thorough knowledge of Surgery-General. When it is time for the Surgery-General board and certification exam, you will already be ready. Besides online study quizzes, we also publish our peer-reviewed content in eBooks and mobile Apps. We also offer inexpensive CME/CE, so our content can be used to attain education credits while you study Surgery-General.

redpajama_set_name: RedPajamaCommonCrawl


text:
Aleksandr Aleksandrowicz Samonow, ros. Александр Александрович Самонов (ur. 23 sierpnia 1995 w Moskwie) – rosyjski hokeista, reprezentant Rosji, olimpijczyk.

Kariera

Wychowanek klubu Krylja Sowietow Moskwa. Karierę rozwijał w Czechowie, grając w zespole juniorskim w lidze MHL, w drużynach stowarzyszonych w WHL, a także w ekipie Witiazia w KHL, już po przeniesieniu klubu do Podolska. Wcześniej bywał tylko w składach meczowych Czechowa w 2021 i Podolska w 2016, a zadebiutował w KHL 11 stycznia 2018. W trakcie sezonu KHL (2019/2020) w połowie października 2019 został przetransferowany do SKA Sankt Petersburg. W grudniu tego roku przedłużył tam umowę o trzy lata.

W barwach Rosji uczestniczył w turnieju zimowej uniwersjady edycji 2018. W składzie reprezentacji Rosyjskiego Komitetu Olimpijskiego (ang. ROC) brał udział w turnieju MŚ edycji 2021. W barwach reprezentacji Rosyjskiego Komitetu Olimpijskiego uczestniczył w turnieju zimowych igrzysk olimpijskich 2022.

Sukcesy
 Reprezentacyjne
  Złoty medal zimowej uniwersjady: 2015
  Srebrny medal zimowych igrzysk olimpijskich: 2022

 Klubowe
  Złoty medal WHL /  Puchar Pietrowa: 2018 z Dinamem Sankt Petersburg
  Srebrny mistrzostw Rosji: 2020 (uznaniowo) z SKA Sankt Petersburg

 Indywidualne
 Wysszaja Chokkiejnaja Liga (2017/2018):
 Trzecie miejsce w klasyfikacji skuteczności interwencji w sezonie zasadniczym: 94,6%
 Pierwsze miejsce w klasyfikacji średniej straconych goli na mecz w sezonie zasadniczym: 1,17
 Pierwsze miejsce w klasyfikacji liczby straconych goli w sezonie zasadniczym: 10
 Pierwsze miejsce w klasyfikacji skuteczności interwencji w fazie play-off: 94,4%
 Drugie miejsce w klasyfikacji średniej straconych goli na mecz w fazie play-off: 1,57
 Drugie miejsce w klasyfikacji liczby straconych goli w fazie play-off: 3
 Najlepszy bramkarz tygodnia - 19 września 2017, 25 września 2017, 12 grudnia 2017
 Najlepszy bramkarz miesiąca - wrzesień 2017, październik 2017
 Najbardziej Wartościowy Zawodnik (MVP) w fazie play-off
 Najlepszy bramkarz sezonu
 KHL (2019/2020):
 Pierwsze miejsce w klasyfikacji skuteczności interwencji w sezonie zasadniczym: 94,7%
 Czwarte miejsce w klasyfikacji średniej straconych goli na mecz w sezonie zasadniczym: 1,51
 Najlepszy bramkarz tygodnia - 4 lutego 2020
 Mecz Gwiazd KHL (wybrany, nie zagrał)
 Mistrzostwa Świata w Hokeju na Lodzie 2021 (elita):
 Trzecie miejsce w klasyfikacji skuteczności interwencji w turnieju: 94,37%
 Drugie miejsce w klasyfikacji średniej straconych goli na mecz w turnieju: 1,32
 Jeden z trzech najlepszych zawodników reprezentacji w turnieju

Przypisy

Bibliografia

 Aleksandr Samonow – profil na stronie MHL
 Aleksandr Samonow – profil na stronie WHL
 Aleksandr Samonow – profil na stronie KHL

Hokeiści Russkich Witiaziów Czechow
Hokeiści THK Twer
Hokeiści Dinama Sankt Petersburg
Hokeiści Witiazia Podolsk
Hokeiści SKA Sankt Petersburg
Ludzie urodzeni w Moskwie
Medaliści Zimowej Uniwersjady 2017
Medaliści Zimowych Igrzysk Olimpijskich 2022
Rosyjscy hokeiści
Rosyjscy medaliści olimpijscy
Urodzeni w 1995

redpajama_set_name: RedPajamaWikipedia


text:
\section*{Appendix A.}
\label{app:theorem}

\begin{proof}[Proof of Theorem~\ref{thm: upper_bd}]
We first state without proof a crucial lemma from \cite{lattimore_szepesvari_2020} which we will use in our analysis.
\begin{lemma}[\citet{lattimore_szepesvari_2020}]
\label{subthm: lattimore_main}
\em Let $\PP_t(\, \cdot \, ) = \PP(\, \cdot \,  | A_1,X_1,\dots,A_{t-1},X_{t-1})$ be the probability measure conditioned on the history up to time $t-1$ and $G_{is} = \PP_t(E_i^c(t) | T_{i,t} = s)$, where $E_i(t)$ is any specified event for arm $i$ at time $t$. Then $$\EE[T_{i,n}] \leq \sum_{s=0}^{n-1} \EE \parenb{\frac{1}{G_{1s}} - 1} +  \sum_{s=0}^{n-1} \PP \paren{G_{is} > \frac{1}{n}} + 1.$$
\end{lemma}
Denote the sample entropic risk at $\gamma$ by $\widehat{\ER}(i,t) = -\theta_{i,t} + \gamma / (2 \kappa_{i,t})$. Fix $\eeps > 0$, and define
\begin{equation*}
	E_i(t) := \sett{\widehat{\ER}(i,t) > \ER_{\gamma}(1) + \eeps},
\end{equation*}
the event that the Thompson sample entropic risk of arm $i$ is $\eeps$-higher than the optimal arm (which has the lowest entropic risk). Intuitively, event $E_i(t)$ is highly likely to occur when the algorithm has explored sufficiently. However, the algorithm does not choose arm $i$ when $E_i^c(t)$, an event with small probability under Thompson sampling, occurs. By Lemma~\ref{subthm: lattimore_main} and the linearity of expectation, we can divide $\EE[T_{i,n}]$ into two parts as
\begin{equation}
\label{eqn: key_lemma}
\EE[T_{i,n}] \leq \sum_{s=0}^{n-1} \EE \parenb{\frac{1}{G_{1s}} - 1} +  \sum_{s=0}^{n-1} \PP \paren{G_{is} > \frac{1}{n}} + 1.\end{equation}
By Lemmas~\ref{lem: upper_bound_term_1_risk} and \ref{lem: upper_bound_term_2_risk} by that which follows, we have
\begin{align*}
\sum_{s=1}^{n} \EE \parenb{\frac{1}{G_{1s}} - 1} &\leq \frac{C_1}{\eeps^3} + \frac{C_2}{\eeps^2} + \frac{C_3}{\eeps} + C_4,\ \text{and}\\
\sum_{s=1}^n \PP_t\paren{G_{is} > \frac{1}{n}}
&\leq 1 + \max \sett{\frac{2\log (2n)}{\xi^2\paren{\ERgap{i} - \eeps}^2}, \frac{\log(2n)}{h \paren{\frac{\gamma \sigma^2}{\gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)}}}} + \frac{C_5}{\eeps^4} + \frac{C_6}{\eeps^2}.
\end{align*}
Plugging the two displays into (\ref{eqn: key_lemma}), we have
\begin{equation}
	\EE[T_{i,n}] \leq 1 + \max \sett{\frac{2 \log (2n)}{\xi^2\paren{\ERgap{i} - \eeps}^2}, \frac{\log(2n)}{h \paren{\frac{\gamma \sigma^2}{\gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)}}}} + \frac{C_1'}{\eeps^4} + \frac{C_2'}{\eeps^3} + \frac{C_3'}{\eeps^2} + \frac{C_4'}{\eeps} + C_5', \label{eqn: pre_result}
\end{equation}
where $C_1',C_2',C_3',C_4',C_5'$ are constants. Setting $\eeps = {(\log n)}^{-\frac{1}{8}}$ into (\ref{eqn: pre_result}), we get
\begin{align*}
\limsup_{n\to\infty}\frac{\ccal R_{n}{(\text{ERTS})}}{\log n}
&\leq \sum_{i \in \sdiff{[K]}{\sett{1}}} \paren{\max \sett{\frac{2}{\xi^2\Delta_{\mathrm{ER}}^2(i)}, \frac{1}{h \paren{\frac{\gamma \sigma^2}{ \gamma \sigma_i^2-2(1-\xi)\ERgap{i}}}}}}\ERgap{i}.
\end{align*}
\end{proof}

\begin{lemma}
\label{lem: tail_lower_bd}
\em We can lower bound
\begin{equation*}
 	\PP_t\paren{E_1^c(t) \mid T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma}=\PP_t\paren{\widehat\ER_1 \leq \ER_1 + \varepsilon \mid T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma}
 \end{equation*}
by
\begin{align}
&\PP_t\paren{\widehat\ER_i \leq \ER_1 + \varepsilon \mid T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma} \nonumber\\
&\geq \begin{cases}
 	\PP_t\paren{{\theta}_{1,t} - \mu_1\geq -\frac{\eeps}{2}} \cdot \PP_t \paren{\frac{1}{{\kappa_{1,t}}}-\sigma_1 \leq \frac{\eeps}{\gamma}} &\text{if } \mu \leq \mu_1, \sigma \geq \sigma_1,\\
 	\frac{1}{2} \PP_t \paren{\frac{1}{{\kappa_{1,t}}}-\sigma_1 \leq \frac{\eeps}{\gamma}} &\text{if } \mu > \mu_1, \sigma \geq \sigma_1,\\
 	\frac{1}{2} \PP_t\paren{{\theta}_{1,t} - \mu_1\geq -\frac{\eeps}{2}} &\text{if } \mu \leq \mu_1, \sigma < \sigma_1,\\
 	\frac{1}{4} &\text{if } \mu > \mu_1, \sigma < \sigma_1.
 \end{cases}\label{eqn: lower_bd}
\end{align}
\end{lemma}

\begin{proof}
Given $T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma$, a direct calculation gives us,
\begin{align*}
&\PP_t\paren{\widehat\ER_1 \leq \ER_1 + \varepsilon \mid T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma} \nonumber\\
&= \PP_t\paren{-\theta_{1,t} + \frac{\gamma}{2\kappa_{1,t}}- \bp{-\mu_1 + (\gamma/2)\sigma_1^2} \leq  \varepsilon\ \Big|\ T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma}\\
&= \PP_t\paren{-(\theta_{1,t} - \mu_1) + \frac{\gamma}{2}\bp{\frac{1}{\kappa_{1,t}} - \sigma_1^2} \leq  \varepsilon\ \Big|\ T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma}\\
&\geq \PP_t\paren{-(\theta_{1,t} - \mu_1)  \leq  \varepsilon/2 \mid T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma}\\ &\quad \; \PP_t\paren{ \frac{\gamma}{2}\bp{\frac{1}{\kappa_{1,t}} - \sigma_1^2} \leq  \varepsilon/2 \ \Big|\ T_{1,t} = s, \hat{\mu}_{1,s} = \mu, \hat{\sigma}_{1,s} = \sigma}\\\
&\geq \begin{cases}
 	\PP_t\paren{{\theta}_{1,t} - \mu_1\geq -\frac{\eeps}{2}} \cdot \PP_t \paren{\frac{1}{{\kappa_{1,t}}}-\sigma_1^2 \leq \frac{\eeps}{\gamma}} &\text{if } \mu \leq \mu_1, \sigma^2 \geq \sigma_1^2,\\
 	\frac{1}{2} \PP_t \paren{\frac{1}{{\kappa_{1,t}}}-\sigma_1^2 \leq \frac{\eeps}{\gamma}} &\text{if } \mu > \mu_1, \sigma^2 \geq \sigma_1^2,\\
 	\frac{1}{2} \PP_t\paren{{\theta}_{1,t} - \mu_1\geq -\frac{\eeps}{2}} &\text{if } \mu \leq \mu_1, \sigma^2 < \sigma_1^2,\\
 	\frac{1}{4} &\text{if } \mu > \mu_1, \sigma^2 < \sigma_1^2.
 \end{cases}\label{eqn: lower_bd}
\end{align*}
Then the lemma holds since $\PP_t(\theta_{1,t} - \mu_1 \geq - \eeps/2) > 1/2$ if $\mu > \mu_1$, and $\PP_t \paren{\frac{1}{\kappa_{1,t}} - \sigma_1^2 \leq \frac{\eeps}{\gamma}} \geq 1/2$ if $\sigma < \sigma_1^2$, by using properties of the median of the Gaussian and Gamma distributions respectively.

\end{proof}

\begin{lemma}[Upper bounding the first term of (\ref{eqn: key_lemma})]
\label{lem: upper_bound_term_1_risk}
\em We have \begin{equation*}
		\sum_{s=1}^{n} \EE \parenb{\frac{1}{G_{1s}} - 1} \leq \frac{C_1}{\eeps^2} + \frac{C_2}{\eeps} + C_3,
	\end{equation*}
	where $C_1,C_2,C_3$.
\end{lemma}
\begin{proof}
The proof follows immediately from Lemma~\ref{lem: tail_lower_bd} and \citet[S-3.3]{zhu2020thompson} by scaling $\eeps >0$.
\end{proof}

\begin{lemma}\label{lem: tail_upper_bd}
\em For $\xi \in (0,1)$, we have
\begin{align*}
    &\PP\paren{\widehat\ER_i \leq \ER_1 + \varepsilon \mid T_{i,t} = s, \hat{\mu}_{i,t} = \mu, \hat{\sigma}_{i,t}^2 = \sigma^2}\\
    &\leq \exp \paren{-\frac{s}{2}\paren{\mu_i - \mu + \xi (\ERgap{i} - \varepsilon)}^2} + \exp \paren{-sh \paren{\frac{\gamma \sigma^2}{ \gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)}}},
\end{align*}
where $h(x) = \frac{1}{2}(x-1-\log x)$.
\end{lemma}
\begin{proof}
For $\xi \in (0,1)$, we have
\begin{align*}
    &\PP\paren{\widehat\ER_i \leq \ER_1 + \varepsilon \mid T_{i,t} = s, \hat{\mu}_{i,t} = \mu, \hat{\sigma}_{i,t}^2 = \sigma^2}\\

     &= \PP_t\paren{-\theta_{i,t} +\mu_i + \frac{\gamma}{2}\bp{\frac{1}{\kappa_{i,t}} - \sigma_i^2} \leq -\ERgap{i} + \varepsilon \ \Big|\ T_{i,t} = s, \hat{\mu}_{i,s} = \mu, \hat{\sigma}_{i,s} = \sigma}\\
     &\leq \PP_t\paren{-\theta_{i,t} +\mu_i \leq -\xi\bp{\ERgap{i} - \varepsilon}\mid T_{i,t} = s, \hat{\mu}_{i,s} = \mu, \hat{\sigma}_{i,s} = \sigma} +\\ &\quad\; \PP_t\paren{ \frac{\gamma}{2}\bp{\frac{1}{\kappa_{i,t}} - \sigma_i^2} \leq -(1-\xi)\bp{\ERgap{i} - \varepsilon} \ \Big|\ T_{i,t} = s, \hat{\mu}_{i,s} = \mu, \hat{\sigma}_{i,s} = \sigma}\\

     &= \PP_t\paren{\theta_{i,t} - \mu \geq (\mu_i -\mu) + \xi\bp{\ERgap{i} - \varepsilon}\mid T_{i,t} = s, \hat{\mu}_{i,s} = \mu, \hat{\sigma}_{i,s} = \sigma} +\\ &\quad\; \PP_t\paren{ \kappa_{i,t} \geq \frac{\gamma}{  \gamma\sigma_i^2-2(1-\xi)\bp{\ERgap{i} - \varepsilon}} \ \Big|\ T_{i,t} = s, \hat{\mu}_{i,s} = \mu, \hat{\sigma}_{i,s} = \sigma}\\
      &\leq \exp \paren{-\frac{s}{2}\paren{\mu_i - \mu + \xi (\ERgap{i} - \varepsilon)}^2} + \exp \paren{-sh \paren{\frac{\gamma \sigma^2}{\gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)}}},
\end{align*}
where $h(x) = \frac{1}{2}(x-1-\log x)$.
\\\\
The lemma holds by the Chernoff upper bound for $\PP_t(\theta_{i,t} \geq \cdot )$ and Lemma~\ref{lem: harre} below to upper-bound $\PP_t(\kappa_{i,t} \geq \cdot)$.

\begin{lemma}[\citet{Harremo_s_2017}]
\label{lem: harre}
\em For a Gamma r.v. $X \sim \mathrm{Gamma}(\alpha,\beta)$ with shape $\alpha \geq 2$ and rate $\beta > 0$, we have $$\PP(X \geq x) \leq \exp \paren{-2\alpha h \paren{\frac{\beta x}{\alpha}}},\ x > \frac{\alpha}{\beta},$$ where $h(x) = \frac{1}{2}(x-1-\log x)$.
\end{lemma}
\end{proof}

\begin{lemma}[Upper bounding the second term of (\ref{eqn: key_lemma})]
\label{lem: upper_bound_term_2_risk}
\em We have
\begin{align*}
\sum_{s=1}^n \PP_t\paren{G_{is} > \frac{1}{n}}
&\leq 1 + \max \sett{\frac{2\log (2n)}{\xi^2\paren{\ERgap{i} - \eeps}^2}, \frac{\log(2n)}{h \paren{\frac{\gamma \sigma^2}{ \gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)}}}} + \frac{C_4}{\eeps^4} + \frac{C_5}{\eeps^2},
\end{align*}
where $C_4,C_5$ are constants.
\end{lemma}
\begin{proof}
Following from Lemma~\ref{lem: tail_upper_bd}, we have the following inclusions:
\begin{align*}
    &\sett{ {\hat \mu_{i,t} + \sqrt{\frac{2\log 2n}{s}} \leq \mu_i + \xi {(\ERgap{i} - \varepsilon)}}}\\
    &\subseteq \sett{\exp \paren{-\frac{s}{2}\paren{\mu_i - \mu + \xi (\ERgap{i} - \varepsilon)}^2} \leq \frac{1}{2n}}
\end{align*}
and
\begin{align*}
    &\sett{\frac{\gamma \hat \sigma_{i,t}^2}{\gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)} \leq \inv {h_-}\paren{\frac{\log 2n}{s}}}\\
    &\cup \sett{\frac{\gamma \hat \sigma_{i,t}^2}{ \gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)} \geq \inv {h_+}\paren{\frac{\log 2n}{s}}}\\
    &\subseteq \sett{\exp \paren{-sh \paren{\frac{\gamma \sigma^2}{\gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon) }}} \leq \frac{1}{2n}},
\end{align*}
where $\inv {h_+}(y) = \max \sett{x : h(x) = y}$ and $\inv {h_-}(y) = \min \sett{x : h(x) = y}$. Hence, for $$s \geq u = \max \sett{\frac{2\log (2n)}{\xi^2\paren{\ERgap{i} - \eeps}^2}, \frac{\log(2n)}{h \paren{\frac{\gamma \sigma^2}{\gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)}}}},$$
 by replacing $\paren{\mu_1 - \eeps,\frac{\hat\sigma_i^2}{\sigma_1^2+\eeps}}$ with $\paren{\mu_i + \xi \paren{\ERgap{i} - \eeps},\frac{\gamma \hat \sigma_{i,t}^2}{ \gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)}}$ in \citet[S-3.4]{zhu2020thompson}, we get $$\PP_t\paren{G_{is}>\frac{1}{n}} \leq \exp\paren{-\frac{s\eeps^2}{\sigma_i^2}} + \exp\paren{-(s-1) \frac{\eeps^2}{\sigma_i^4}}.$$
 Summing over $s$,
 \begin{align*}
     &\sum_{s=1}^n \PP_t\paren{G_{is} > \frac{1}{n}}\ \leq u + \sum_{s = \lceil u \rceil}^n \parenb{\exp\paren{-\frac{s\eeps^2}{\sigma_i^2}} + \exp\paren{-(s-1) \frac{\eeps^2}{\sigma_i^4}}}\\
&\leq 1 + \max \sett{\frac{2\log (2n)}{\xi^2\paren{\ERgap{i} - \eeps}^2}, \frac{\log(2n)}{h \paren{\frac{\gamma \sigma^2}{\gamma \sigma_i^2-2(1-\xi)(\ERgap{i} - \varepsilon)}}}} + \frac{C_4}{\eeps^4} + \frac{C_5}{\eeps^2}.
 \end{align*}
Finally, set $$\xi_\gamma = 1 - \frac{\gamma \sigma_i^2}{2\ERgap{i}} \paren{1-\frac{1}{\inv {h_+}\paren{ \Delta_{\mathrm{\ER}}^2(i,\gamma)/2}}} \in (0,1),$$ where $\inv {h_+}(y) = \max \sett{x : h(x) = y}$. By algebra,
\begin{align*}
    &h \paren{\frac{\gamma \sigma_i^2}{\gamma \sigma_i^2-2(1-\xi_\gamma)\ERgap{i}}}\\
    &= h \paren{\frac{\gamma \sigma_i^2}{\gamma \sigma_i^2-2\cdot \frac{\gamma \sigma_i^2}{2\ERgap{i}} \paren{1-\frac{1}{\inv {h_+}\paren{ \Delta_{\mathrm{\ER}}^2(i,\gamma)/2}}} \cdot \ERgap{i}}}\\
    &= h \paren{\frac{\gamma \sigma_i^2}{ \gamma \sigma_i^2 - \gamma \sigma_i^2\paren{1-\frac{1}{\inv {h_+}\paren{ \Delta_{\mathrm{\ER}}^2(i,\gamma)/2}}} }} = h \paren{\frac{\gamma \sigma_i^2}{ \paren{\frac{\gamma \sigma_i^2}{\inv {h_+}\paren{ \Delta_{\mathrm{\ER}}^2(i,\gamma)/2}}}}}\\
    &= h \paren{\inv {h_+}\paren{ \Delta_{\mathrm{\ER}}^2(i,\gamma)/2}} = \Delta_{\mathrm{\ER}}^2(i,\gamma)/2 \geq \xi_\gamma^2\Delta_{ \mathrm{\ER}}^2(i,\gamma)/2
\end{align*}
which implies $$\frac{1}{h \paren{\frac{\gamma \sigma_i^2}{ \gamma \sigma_i^2-2(1-\xi_\gamma)\ERgap{i}}}} \leq \frac{2}{\xi_\gamma^2\Delta_{\ER}^2(i)}.$$ and $\xi_\gamma \to 1^-$ as $\gamma \to 0^+$.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{thm: lower_bd}]
We note that for any arm $i$ with distribution $\nu(i) \sim \mathcal N(\mu_i,\sigma_i^2)$ and $\nu'(i) \sim \mathcal N(\mu_i', {(\sigma_i')}^2)$, the KL-divergence given by $$\KL(\nu(i),\nu'(i)) = \log \frac{\sigma_i'}{\sigma_i} + \frac{\sigma_i^2 + {(\mu_i-\mu_i')}^2}{2{(\sigma_i')}^2} - \frac{1}{2}$$ is well-known. Denote $\mathcal S_i = \sett{\nu'(i) \in {\mathcal E}_{\mathcal N}^K : \ER(\nu'(i)) < \ER(1)}$. Denote $$R_i := \max \left\{\frac{2}{\xi^2\Delta_{\ER}^2(i)},\frac{1}{h \paren{\frac{\gamma \sigma^2}{\gamma \sigma_i^2-2(1-\xi)\ERgap{i}}}}\right\} > 0,$$ and fix $\eeps > 0$ and consider the arm with the distribution $\mathcal{N} \paren{\mu_i+\sigma_i \sqrt{2/R_i}+\eeps, \sigma_i^2}$. Then a direct computation gives
\begin{align*}
    \ER(\nu'(i)) - \ER(\nu(1))
    &= -(\mu_i +\sigma_i \sqrt{2/R_i}+ \eeps) + \frac{\gamma}{2}\sigma_i^2 - \paren{-\mu_i + \frac{\gamma}{2}\sigma_i^2}\\
    &= - (\sigma_i \sqrt{2/R_i}+\eeps) < 0,
\end{align*}
thus $ \ER(\nu'(i)) < \ER(\nu(1))$ and  $\nu'(i) \in \mathcal{S}_i$. Furthermore,
\begin{align*}
    \KL(\nu(i), \nu'(i)) &= \log \frac{\sigma_i}{\sigma_i} + \frac{\sigma_i^2 + \paren{\mu_i - \paren{\mu_i + \sigma_i \sqrt{2/R_i} + \eeps}}^2}{2\sigma_i^2} - \frac{1}{2}\\
    &= \frac{1}{R_i} + \frac{(2 \sigma_i \sqrt{2/R_i}  + \eeps)\eeps}{2\sigma_i^2}.
\end{align*}
By the definition of $\eta$, $$\eta(i,\gamma) \leq \lim_{\eeps \to 0^+} \parenb{\frac{1}{R_i} + \frac{(2 \sigma_i \sqrt{2/R_i}  + \eeps)\eeps}{2\sigma_i^2}} = \frac{1}{R_i} \Longrightarrow \frac{1}{\eta(i,\gamma)} \geq R_i.$$
Hence, $$\liminf_{n \to \infty} \frac{\mathcal R_n(\pi)}{\log n} = \sum_{i \in \sdiff{[K]}{\sett{1}}} \paren{\liminf_{n \to \infty} \frac{\EE[T_{i,n}]}{\log n}} \ERgap{i} \geq \sum_{i \in \sdiff{[K]}{\sett{1}}} R_i \ERgap{i}.$$
Thus, we have that ERTS is asymptotically optimal unconditionally.
\end{proof}
\vskip 0.2in

\section{Conclusion}\label{sec: conc}
This paper applies Thompson sampling \citep{thompson1933likelihood} to provide the first solution for entropic risk MAB problems which have not been previously considered before to the best of our knowledge. We proposed a new algorithm ERTS to solve this problem and proved that this proposed algorithm is asymptotically optimal for the ER MAB problem. Further work includes analysing Thompson sampling of Gaussian MABs under general risk measures and exploring Thompson sampling's performance for Entropic-Risk sub-Gaussian bandits. We may also potentially design a general framework for proving the efficacy of Thompson sampling over the state-of-the-art L/UCB-based techniques for generalised risk-averse MABs and a wider class of bandits (under reasonable assumptions, such as the crucial properties of the risk-measures, existence of conjugate prior estimates, as well as relevant concentration bounds).
\subsection{Contributions}
\begin{itemize}
    \item \textbf{ERTS Algorithm:}
We design ERTS, an algorithm that is similar to the structure of CVaR-TS in \citet{chang2021riskconstrained} but using entropic risk instead of CVaR as the risk measure. This algorithm uses Thompson sampling \citep{thompson1933likelihood} as explored for mean-variance bandits in \citet{zhu2020thompson} and CVaR bandits in \citet{chang2021riskconstrained}.

    \item \textbf{Comprehensive regret bounds:}
We provide theoretical analysis of the ERTS algorithm for Gaussian bandits with bounded variances. We state and prove both upper and lower bounds, showing that ERTS is the first asymptotically optimal algorithm that solves the entropic risk multi-armed bandit problem. Our proof techniques solidify the novel $\xi$-trick in \citet{chang2021riskconstrained}, and affirm future analysis on MABs involving generalised risk measures.

\end{itemize}

This paper is structured as follows. We first introduce the formulation of the entropic risk MAB problem in Section~\ref{sec: er_mab}. In Section~\ref{sec: er_ts}, we present ERTS algorithm. We present our regret bounds and prove that the upper bound we derived is asymptotically optimal in Section~\ref{sec: regret_bounds}. Section~\ref{sec: pf_outline} provides the proof outlines of the regret bounds in Section~\ref{sec: regret_bounds}. We conclude our discussion in Section~\ref{sec: conc} summarizing our work and suggesting avenues for further research. For brevity, we defer detailed proofs of the theorems to the supplementary material.
\section{Introduction}

The multi-armed bandit (MAB) problem is a classic reinforcement learning problem that analyses sequential decision making, in which the learner has access to partial feedback from her decisions. The problem has been garnering interest in recent years. It informs many critical theoretical questions about the role of exploration vs exploitation in reinforcement learning and applies to both theoretical problems and various real-world applications, such as dynamic pricing, clinical trials, and portfolio optimisation.
\\\\
In the well-known stochastic MAB setting, a player chooses among $K$ arms, each characterised by an independent reward distribution. During each period, the player plays one arm and observes a random reward from that arm. She then incorporates the information she receives from pulling that arm in choosing the next arm she selects. The player repeats the process for a horizon of $n$ periods. In each period, the player faces a dilemma between exploring other arms' potential value or exploiting the arm that the player believes offers the highest estimated reward.
\\\\
In the usual setting, the risk of pulling an arm is not being taken into account. However, in many practical settings, such as financial portfolio optimisation, the risk is often the clients' main concern. In this regard, the MAB problem can been tweaked to model such risk-aversion. This paper uses entropic risk measure as the risk measure to minimise due to the simple exponential relationship it has with risk-aversion and utility, and devises a Thompson sampling-based learning algorithm that minimises entropic risk.
\section{The ERTS Algorithm}\label{sec: er_ts}
In this section, we introduce the Entropic Risk Thompson Sampling (ERTS) algorithm for Gaussian bandits with bounded variances, i.e., $\nu \in \ccal E_{\ccal N}^K(\sigma_{\max}^2) := \{\nu=(\nu_1,\dots,\nu_K) : \nu_i \sim \ccal N(\mu_i,\sigma_i^2), \sigma_i^2 \leq \sigma_{\max}^2\ \forall i \in [K]\}$ for some $\sigma_{\max}^2 > 1$. Similar to \citet{zhu2020thompson} and \citet{chang2021riskconstrained}, the algorithm samples from the posteriors of each arm, then chooses the arm according to a multi-criterion procedure.
\\\\
Denote the mean and precision of the Gaussian by $\mu$ and $\psi$ respectively. If $(\mu,\psi)$ follows the distribution $\mathrm{Normal}\text{-}\mathrm{Gamma}(\mu,T,\alpha, \beta)$, then $\psi \sim \mathrm{Gamma}(\alpha,\beta)$, and $\mu | \psi \sim \ccal N(\mu,1/(\psi T))$. Since the conjugate prior for the Gaussian with unknown mean and variance is the Normal-Gamma distribution, we use Algorithm~\ref{alg: update} to update $(\mu,\psi)$ via Bayes' theorem.
\\\\
We present the ERTS algorithm. In each round $t$, for each arm $i$, the player samples the parameters $(\theta_{it},\kappa_{it})$ from the posterior distribution of arm $i$, then chooses arm $j = \argmin_{i \in [k]} \widehat{\ER}_\gamma(i,t)$, where $\widehat{\ER}_\gamma(i,t) := -\theta_{i,t} + \gamma/(2 \kappa_{i,t})$, i.e. least risky arm available.
\begin{algorithm}[ht]
  \caption{$\Update(\hat{\mu}_{i,t-1}, T_{i,t-1}, \alpha_{i,t-1}, \beta_{i,t-1})$}
  \label{alg: update}
\begin{algorithmic}[1]
	\STATE {\bfseries Input:} Prior parameters $(\hat{\mu}_{i,t-1}$, $T_{i,t-1}$, $\alpha_{i,t-1}$, $\beta_{i,t-1})$ and new sample $X_{i,t}$
	\STATE Update the mean: $\hat{\mu}_{i,t} = \frac{T_{i,t-1}}{T_{i,t-1}+1}\hat{\mu}_{i,t-1} + \frac{1}{T_{i,t-1}+1} X_{i,t}$
	\STATE Update the number of samples, the shape parameter, and the rate parameter: $T_{i,t} = T_{i,t-1} + 1$, $\alpha_{i,t} = \alpha_{i,t-1} + \frac{1}{2}$, $\beta_{i,t} = \beta_{i,t-1} + \frac{T_{i,t-1}}{T_{i,t-1}+1} \cdot \frac{{(X_{i,t} - \hat{\mu}_{i,t-1})}^2}{2}$
\end{algorithmic}
\end{algorithm}
\begin{algorithm}[ht]
  \caption{Entropic Risk Thompson Sampling (ERTS)}
  \label{alg: ERTS}
\begin{algorithmic}[1]
  \STATE {\bfseries Input:} Risk parameter $\gamma$, $\hat{\mu}_{i,0} = 0$, $T_{i,0} = 0$, $\alpha_{i,0} = \frac{1}{2}$, $\beta_{i,0} = \frac{1}{2}$
  \FOR{$t=1,2,\ldots, K$}
  \STATE Play arm $t$ and update $\hat{\mu}_{t,t} = X_{t,t}$
  \STATE $\Update(\hat{\mu}_{t,t-1}, T_{t,t-1}, \alpha_{t,t-1}, \beta_{t,t-1})$
  \ENDFOR
  \FOR{$t=K+1,K+2,...$}
  \STATE Sample $\kappa_{i,t}$ from $\mathrm{Gamma}(\alpha_{i,t-1},\beta_{i,t-1})$
  \STATE Sample $\theta_{i,t}$ from $\mathcal{N}(\hat{\mu}_{i,t-1}, 1/T_{i,t-1})$
  \STATE Play arm $j(t) = \argmin_{i \in [K]} \widehat{\ER}_{\gamma}(i,t)$ and observe loss $X_{j(t),t}\sim \nu(j(t))$
  \STATE $\Update(\hat{\mu}_{j(t),t-1}, T_{j(t),t-1}, \alpha_{j(t),t-1}, \beta_{j(t),t-1})$
  \ENDFOR
\end{algorithmic}
\end{algorithm}

\input{regret_bounds}
\section{Proof Outlines for Theorem~\ref{thm: upper_bd} and \ref{thm: lower_bd}}\label{sec: pf_outline}
Theorem~\ref{thm: upper_bd}: Denote the sample entropic risk as $\hat{\ER}_{\gamma}(i,t) = -\theta_{i,t} + {\gamma}/{(2\kappa_{i,t})}$. Fix
$\eeps > 0$ and define $E_i(t) := \bb{\hat{\ER}_{\gamma}(i,t)> \ER_{\gamma}(1) + \eeps}$, that is, the event that the Thompson sample mean of arm $i$ is $\eeps$-riskier than a certain threshold or, more precisely, $\eeps$-higher than the optimal arm (which has the lowest entropic risk). Intuitively, event $E_i(t)$ occurs with high probability when the algorithm has explored sufficiently. However, the algorithm does not choose arm $i$ when $E_{i}^c(t)$ occurs with small probability under Thompson sampling, which contributes directly to the regret bound. Therefore, it suffices to bound the number of times $E_{i}^c(t)$ occurs.
\\\\
In order to bound $\E{T_{i,n}}$, we can split $\E{T_{i,n}}$ into two parts using a key lemma by \citet{lattimore_szepesvari_2020} to yield $\E{T_{i,n}} \leq \Lambda_1 + \Lambda_2 +1$, where $\Lambda_1 = \E{\sum^{n-1}_{s=0}\bp{\frac{1}{G_{1,s}}-1}}$ and  $\Lambda_2 = \sum^{n-1}_{s=0}\mathbb{P}\bp{G_{1,s} > \frac{1}{n}}$. It remains to upper bound $\Lambda_1$ and $\Lambda_2$. The techniques to upper bound $\Lambda_1$ are similar to those from \citet[Section 4.6]{zhu2020thompson} and \citet[Section 5]{chang2021riskconstrained}. To upper bound $\Lambda_2$, we split the event $E_i^{c}(t) = \bp{\hat{\ER}_{\gamma}(i,t) \leq \ER_{\gamma}(1) + \eeps}$ into
\begin{align*}
    \Psi_1(\xi) &= \bb{-\theta_{i,t} +\mu_{i} \leq -\xi(\Delta_{\mathrm{ER}}(i,\gamma) - \eeps)}, \\
    \Psi_2(\xi) &= \bb{\frac{\gamma}{2}\paren{\frac{1}{\kappa_{i,t}} - \sigma_{i}^2} \leq (-1+\xi)(\Delta_{\mathrm{ER}}(i,\gamma) - \eeps)}
\end{align*}
That is, $E_{i}^c(t) \subseteq \Psi_1(\xi) \cup \Psi_2(\xi)$. We then use the union bound which yields $\mathbb{P}(E^c_{i}(t))\leq \PP (\Psi_1(\xi)) + \PP (\Psi_2(\xi))$, which we can upper bound by known concentration bounds. Following the strategy employed by \citet{chang2021riskconstrained}, a judicious selection of the free parameter $\xi \in (0,1)$ allows us to allocate "weights" on the bounds of $\PP(\Psi_1(\xi))$ and $\PP(\Psi_2(\xi))$ which then yield $ {2}/{(\xi^2\Delta_{\ER}^2(i,\gamma))}$ and $\paren{h \paren{\frac{\gamma \sigma_i^2}{\gamma \sigma_i^2-2(1-\xi)\ERgap{i}}}}^{-1}$ without incurring further residual terms.
\\\\
Theorem~\ref{thm: lower_bd}: The proof of the lower bound follows immediately from \citet[Theorem 4]{kagrecha2020constrained} by replacing the criterion $c_\alpha(\nu'(k)) \leq c_\alpha^*$ by $\ER(\nu'(k)) \leq \ER(1)$. We then particularize the lower bounds therein by decisively setting the distribution of $\nu'(i)$ to have a Gaussian distribution with mean $\mu_i+\sigma_i \sqrt{2/R_i}+\eeps$ and variance $\sigma_i^2$, which then returns the desired lower bound.
\input{conclusion}
\newpage

\section{Problem formulation}\label{sec: er_mab}
In this section we define the entropic risk MAB problem. For the rest of the paper, denote $[k] = \{1,\dots,k\}$ for any $k \in \NN$ and ${(t)}^+ = \max\{0,t\}$ for $t \in \RR$.
\begin{definition}
\em For any random variable $X$, given a risk parameter $\gamma$, the \emph{entropic risk} \citep{lee2020learning, Howard72} of $X$ is defined by $$\ER_\gamma(X) := \frac{1}{\gamma} \log \EE[\exp(-\gamma X)].$$
\end{definition}
In this paper, we work with Gaussian random variables $X \sim \ccal N(\mu,\sigma^2)$. Direct computations then yield $\ER_\gamma(X) = -\mu + (\gamma/2) \sigma^2$, which is consistent with the computation in \citet[Section 5]{chang2021riskconstrained}. Setting $\gamma \to 0^+$ (resp. $\gamma \to +\infty$) yields the risk-neutral (resp. risk-averse) setting, since $\mu$ (resp. $\sigma^2$) dominates in the former (resp. latter) case.
\\\\
Consider a $K$-armed MAB $\nu = {(\nu(i))}_{i \in [K]}$ played over a horizon of length $n$. Letting $\ER_\gamma(X)$ denote the entropic risk, our objective is to select the least risky arm, that is, the arm with the lowest entropic risk. Thus, we define an arm $i$ to be optimal precisely when $i \in \argmin_{k \in [K]} \ER_\gamma(\nu(k))$. Suppose arm $1$ is optimal (uniquely, without loss of generality). We can then define $\ERgap{i} := \ER_\gamma(i) - \ER_\gamma(1) > 0$ and the \emph{regret} of a policy $\pi$ by $$\ccal R_n(\pi) := \sum_{i \in \sdiff{[K]}{\{1\}}} \EE[T_{i,n}] \ERgap{i},$$ where $T_{i,n}$ denotes the number of times arm $i$ was pulled in the first $n$ rounds. This is a natural definition based on regret decomposition \citep[Chapter 4.5]{lattimore_szepesvari_2020}, and in fact corresponds to the regret decomposition in the case $\gamma \to 0^+$ (i.e. the risk-neutral setting). In the following, we design and analyse ERTS, which aims to minimise $\ccal R_n(\pi)$, and also attain an instance-dependent lower bound, which establishes asymptotic optimality.
\section{Regret Bound for ERTS and Lower Bounds}\label{sec: regret_bounds}
We present our regret bounds in the following theorems. These verify the conjecture made in \citet[Section 5]{chang2021riskconstrained} regarding risk measures of Gaussian bandits of the form $af(\mu) + b g(\sigma^2)$, where $(f(x),g(x),a,b) = (x,x,-1,\gamma/2)$. Furthermore, they establish ERTS as asymptotically optimal in the context of Gaussian entropic risk bandits.
\begin{theorem}[Upper Bound]\label{thm: upper_bd}
    \em Fix $\xi \in (0,1)$, $\gamma \in (0,\infty)$. Then the asymptotic regret of ERTS for entropic risk Gaussian MAB bandits satisfies $$\limsup_{n \to \infty} \frac{\ccal R_n(\text{ERTS})}{\log n} \leq \sum_{i \in \sdiff{[K]}{\sett{1}}} R_i \ERgap{i},$$
    where
    $$R_i := \max \left\{\frac{2}{\xi^2\Delta_{\ER}^2(i,\gamma)},\frac{1}{h \paren{\frac{\gamma \sigma_i^2}{\gamma \sigma_i^2-2(1-\xi)\ERgap{i}}}}\right\}.$$
    Furthermore, setting $$\xi_\gamma = 1 - \frac{\gamma \sigma_i^2}{2\ERgap{i}} \paren{1-\frac{1}{\inv {h_+}\paren{ \Delta_{\mathrm{\ER}}^2(i,\gamma)/2}}},$$ yields $$\frac{1}{h \paren{\frac{\gamma \sigma_i^2}{ \gamma \sigma_i^2-2(1-\xi_\gamma)\ERgap{i}}}} \leq \frac{2}{\xi_\gamma^2\Delta_{\ER}^2(i)}$$ and $\xi_\gamma \to 1^-$ as $\gamma \to 0^+$, where $\inv {h_+}(y) = \max \sett{x : h(x) = y}$.
\end{theorem}
\begin{remark}
    \em{The final part of the theorem shows that the upper bound is characterised by the quantity ${2}/{(\xi_\gamma^2\Delta_{\ER}^2(i,\gamma))}$. By continuity, we obtain the regret bound ${2}/{(\Delta_{\ER}^2(i,\gamma))}$. Furthermore, we note that $ \ERgap{i} \to -\mu_i - (-\mu_1) = \mu_1 - \mu_i$ as $\gamma \to 0^+$, and thus the upper bound simplifies to $2/{(\mu_1-\mu_i)}^2$. This agrees with our intuition since $\ER_\gamma(i) = -\mu_i + (\gamma/2)\sigma_i^2 \to -\mu_i$ as $\gamma \to 0^+$, implying that we are in the risk-neutral setting. Thus, the results correspond to those derived for mean-variance bandits \citep{zhu2020thompson} and CVaR bandits \citep{chang2021riskconstrained}.}
\end{remark}
Next, we establish an instance-dependent lower bound for the expected pulls of non-optimal arms under consistent algorithms. Consider a class $\ccal C$ of distributions and define $\ccal S_i = \{\nu'(i) \in \ccal C : \ER(\nu'(i)) < \ER(1)\}$. Define for each non-optimal arm $i$, $$\eta(i,\gamma) = \inf_{\nu'(i) \in \ccal S_i} \{\KL(\nu(i),\nu'(i))\},$$ where $\KL(\PP,\PP')$ denotes the \emph{KL-divergence} between two probability measures $\PP,\PP'$.
\begin{theorem}[Lower Bound]\label{thm: lower_bd}
    \em Let $\pi$ be a policy over the class of distributions $\ccal C$ satisfying $\ccal R_n(\pi) = o(n^a)$ for any $a > 0$. Then for any non-optimal arm $i$, we have $$\liminf_{n \to \infty} \frac{\EE[T_{i,n}]}{\log n} \geq \frac{1}{\eta(i,\gamma)}.$$
    In particular, if $\ccal C= \ccal E_{\ccal N}^K(\sigma_{\max}^2)$, then $$\liminf_{n \to \infty} \frac{\ccal R_n(\pi)}{\log n} \geq \sum_{i \in \sdiff{[K]}{\{1\}}} R_i \ERgap{i}.$$
\end{theorem}
\begin{remark}
    {\em This implies that the asymptotic lower bound for the regret matches its asymptotic upper bound in Theorem~\ref{thm: upper_bd} unconditionally. Hence, for the Gaussian entropic risk MAB problem, ERTS is \emph{asymptotically optimal}.}
\end{remark}
\subsection{Related Work}
A variety of analyses on MABs involving risk measures have been carried out. \citet{sani2013riskaversion} considered the mean-variance as their risk measure. Each arm $i$ followed a Gaussian distribution with mean $\mu_i \in [0, 1]$ and variance $\sigma_i^2 \in [0, 1]$. The authors provided an LCB-based algorithm with accompanying regret analyses. \citet{galichet2013exploration} proposed the Multi-Armed Risk-Aware Bandit (\textsc{MaRaB}) algorithm with the goal of minimising the number of pulls of risky arms, using the risk measure CVaR. \citet{Vakili_2016} demonstrated that the instance-dependent and instance-independent regrets in terms of the mean-variance of the reward process over a horizon $n$ are lower bounded by $\Omega(\log n)$ and $\Omega(n^{2/3})$ respectively. \citet{sun2016riskaware} analysed contextual bandits with risk constraints, and developed a meta algorithm which makes use of the online mirror descent algorithm that achieves near-optimal regret with respect to minimising the total cost. \citet{zhu2020thompson} designed the first Thompson sampling algorithm for risk measures, particularly the mean-variance risk measure for Gaussian bandits, and proved near-optimal regret bounds under specific regimes. \citet{chang2021riskconstrained} designed a Thompson sampling algorithm factoring a user's ``risk tolerance'' level, either minimising mean rewards under some ``maximum risk'' criterion, or simply minimising the risk measure. \citet{baudry2020thompson} designed and analysed Thompson sampling-based algorithms $\alpha$-NPTS for bounded rewards and $\alpha$-Multinomial-TS for discrete multinomial distributions.
\\\\
The papers most related to our work is that by \citet{zhu2020thompson} and \citet{chang2021riskconstrained}. \citet{zhu2020thompson} considered arms with the \emph{highest} mean-variance to be optimal, and their definitions and methods can be analogously defined for \emph{minimising} the mean-variance. \citet{chang2021riskconstrained} defined arms with the minimum CVaR as optimal in their ``infeasible instance'', which produced theoretical analogues for ``feasible instances''. This hints that the heavy duty analysis happens in trying to choose arms with the risk measure minimised. Our paper seeks to explore the efficacy of Thompson sampling in the analogous risk-minimising problem setting proposed by  \citet{zhu2020thompson}, but instead considering the \emph{entropic risk} measure. We demonstrate and prove the asymptotic optimality of ERTS, whose asymptotic upper bound matches the theoretical lower bound for consistent algorithms that solve the entropic risk MAB for Gaussian bandits.

redpajama_set_name: RedPajamaArXiv