You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Consider the classical problem of predicting the next bit in a sequence of bits. A standard performance measure is regret (loss in payoff) with respect to a set of experts. For example if we measure performance with respect to two constant experts one that always predicts 0's and another that always predicts 1's it is well known that one can get regret @math with respect to the best expert by using, say, the weighted majority algorithm. But this algorithm does not provide performance guarantee in any interval. There are other algorithms that ensure regret @math in any interval of length @math . In this paper we show a randomized algorithm that in an amortized sense gets a regret of @math for any interval when the sequence is partitioned into intervals arbitrarily. We empirically estimated the constant in the @math for @math upto 2000 and found it to be small -- around 2.1. We also experimentally evaluate the efficacy of this algorithm in predicting high frequency stock data.

Cited Abstract(s):
[1]: We experimentally study on-line investment algorithms first proposed by Agarwal and Hazan and extended by which achieve almost the same wealth as the best constant-rebalanced portfolio determined in hindsight. These algorithms are the first to combine optimal logarithmic regret bounds with efficient deterministic computability. They are based on the Newton method for offline optimization which, unlike previous approaches, exploits second order information. After analyzing the algorithm using the potential function introduced by Agarwal and Hazan, we present extensive experiments on actual financial data. These experiments confirm the theoretical advantage of our algorithms, which yield higher returns and run considerably faster than previous algorithms with optimal regret. Additionally, we perform financial analysis using mean-variance calculations and the Sharpe ratio.

[2]: We present an on-line investment algorithm that achieves almost the same wealth as the best constant-rebalanced portfolio determined in hindsight from the actual market outcomes. The algorithm employs a multiplicative update rule derived using a framework introduced by Kivinen and Warmuth. Our algorithm is very simple to implement and requires only constant storage and computing time per stock in each trading period. We tested the performance of our algorithm on real stock data from the New York Stock Exchange accumulated during a 22-year period. On these data, our algorithm clearly outperforms the best single stock as well as Cover's universal portfolio selection algorithm. We also present results for the situation in which the investor has access to additional "side information." Copyright Blackwell Publishers Inc 1998.

[3]: This paper describes experimental results on using Winnow and Weighted-Majority based algorithms on a real-world calendar scheduling domain. These two algorithms have been highly studied in the theoretical machine learning literature. We show here that these algorithms can be quite competitive practically, outperforming the decision-tree approach currently in use in the Calendar Apprentice system in terms of both accuracy and speed. One of the contributions of this paper is a new variant on the Winnow algorithm (used in the experiments) that is especially suited to conditions with string-valued classifications, and we give a theoretical analysis of its performance. In addition we show how Winnow can be applied to achieve a good accuracy coverage tradeoff and explore issues that arise such as concept drift. We also provide an analysis of a policy for discarding predictors in Weighted-Majority that allows it to speed up as it learns.
Numerous papers (for example [3] [2] [1] ) have implemented algorithms inspired from regret style analysis and applied it on financial and other types of data.