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:
Chemical space is so large that brute force searches for new interesting molecules are infeasible. High-throughput virtual screening via computer cluster simulations can speed up the discovery process by collecting very large amounts of data in parallel, e.g., up to hundreds or thousands of parallel measurements. Bayesian optimization (BO) can produce additional acceleration by sequentially identifying the most useful simulations or experiments to be performed next. However, current BO methods cannot scale to the large numbers of parallel measurements and the massive libraries of molecules currently used in high-throughput screening. Here, we propose a scalable solution based on a parallel and distributed implementation of Thompson sampling (PDTS). We show that, in small scale problems, PDTS performs similarly as parallel expected improvement (EI), a batch version of the most widely used BO heuristic. Additionally, in settings where parallel EI does not scale, PDTS outperforms other scalable baselines such as a greedy search, @math -greedy approaches and a random search method. These results show that PDTS is a successful solution for large-scale parallel BO.

Cited Abstract(s):
[1]: The optimization of expensive-to-evaluate functions generally relies on metamodel-based exploration strategies. Many deterministic global optimization algorithms used in the field of computer experiments are based on Kriging (Gaussian process regression). Starting with a spatial predictor including a measure of uncertainty, they proceed by iteratively choosing the point maximizing a criterion which is a compromise between predicted performance and uncertainty. Distributing the evaluation of such numerically expensive objective functions on many processors is an appealing idea. Here we investigate a multi-points optimization criterion, the multipoints expected improvement ( (q- E I )), aimed at choosing several points at the same time. An analytical expression of the (q- E I ) is given when q = 2, and a consistent statistical estimate is given for the general case. We then propose two classes of heuristic strategies meant to approximately optimize the (q- E I ), and apply them to the classical Branin-Hoo test-case function. It is finally demonstrated within the covered example that the latter strategies perform as good as the best Latin Hypercubes and Uniform Designs ever found by simulation (2000 designs drawn at random for every q ∈ [1,10]).
[1] proposed the following framework for parallel BO: given a set of current observations @math and pending experiments @math , an additional set of fantasies @math can be assumed to be the result of those pending experiments. A step of Bayesian optimization can then be performed using the augmented dataset @math and the acquisition function @math . Two different values are proposed for the fantasies: the , where @math for some constant @math and all @math , and the , where @math is given by the GP predictive mean at @math .