Batched Bayesian optimization by maximizing the probability of including the optimum

TL;DR

The paper tackles batched Bayesian optimization in discrete design spaces, where non-additive batch acquisitions hinder optimal batch selection. It introduces qPO (multipoint Probability of Optimality), an exploitative batch construction that maximizes the probability that the true global optimum lies in the acquired batch, expressible as a sum of per-candidate scores $\Pr(x^* \in \mathcal{X}_{acq}) = \sum_{x_i \in \mathcal{X}_{acq}} \Pr(x^* = x_i) = \sum_i \alpha_i$. Alpha_i are estimated via Monte Carlo from the joint posterior, with practical accelerations by approximating the posterior as a multivariate Gaussian; low-probability events are handled via fallback strategies. The method inherently captures diversity through model covariance and remains competitive with state-of-the-art batched BO approaches in antibiotic discovery and QM9-based molecular design, while offering a simple, deterministic alternative to randomization-based strategies. Limitations include reliance on Monte Carlo estimation and potential degradation under high observation noise, suggesting avenues for analytical approximations and robustness studies.

Abstract

Batched Bayesian optimization (BO) can accelerate molecular design by efficiently identifying top-performing compounds from a large chemical library. Existing acquisition strategies for batch design in BO aim to balance exploration and exploitation. This often involves optimizing non-additive batch acquisition functions, necessitating approximation via myopic construction and/or diversity heuristics. In this work, we propose an acquisition strategy for discrete optimization that is motivated by pure exploitation, qPO (multipoint Probability of Optimality). qPO maximizes the probability that the batch includes the true optimum, which is expressible as the sum over individual acquisition scores and thereby circumvents the combinatorial challenge of optimizing a batch acquisition function. We differentiate the proposed strategy from parallel Thompson sampling and discuss how it implicitly captures diversity. Finally, we apply our method to the model-guided exploration of large chemical libraries and provide empirical evidence that it is competitive with and complements other state-of-the-art methods in batched Bayesian optimization.

Figures (3)

• Figure 1: Exploitative batch design by maximizing the likelihood of including the optimum, in the context of a single Bayesian optimization iteration. First, a probabilistic surrogate model is trained on acquired data. Second, samples are obtained from the joint posterior distribution over all candidates. When direct posterior sampling is impossible or inefficient, a multivariate Gaussian may be modeled from the true posterior to enable approximate posterior sampling. Third, we estimate from these samples the probability that each candidate is the true optimum. Fourth, the batch is populated with candidates most likely to be optimal; in doing so, the proposed strategy maximizes the probability that the batch contains the true optimum. In addition to the sampling-based approach visualized here, we describe alternative methods to approximate acquisition scores in Section \ref{['sec:additional_strategies']}.
• Figure 2: Batch diversity of a model-guided optimization loop for antibiotic discovery. Networks depict selected batches in the first iteration after training on a randomly selected (seed of 7) initial batch of 50 designs with growth inhibition values from wong_discovery_2024. Nodes represent acquired compounds; edges are drawn between pairs with Tanimoto similarity $>$ 0.4. Nodes are positioned using the Fruchterman-Reingold force-directed algorithm fruchterman_graph_1991. Histograms portray the distribution of Tanimoto similarity scores for all pairs in the selected batch.
• Figure 3: Retrieval profile for two model-guided searches of chemical libraries. (A) Retrieval of the top 0.5% (197) designs for the iterative discovery of putative antibiotics (Section \ref{['sec:antibiotics']}). (B) Retrieval of the top 0.01% (14) designs for the iterative discovery of organic materials (Section \ref{['sec:qm9']}). For visibility, top-performing methods based on Tables \ref{['tab:main_ab']} and \ref{['tab:main_qm9']} were selected for visualization. qPO performs on par with state-of-the-art methods for both case studies. qPI is competitive in both case studies, while TS-RSR is competitive primarily in the second case study (B). Shaded regions denote $\pm$ one standard error of the mean across ten runs.