Bayesian Optimization in the wild: Risk-averse and Computationally-effective Decision-making

Abstract

Sequential decision-making in some complex and uncertain environments can be formalized as optimizing a black-box function. For example, in drug design, the aim is to maximize compound efficiency by sequentially searching through the vast space of molecules, or, in tuning a particle accelerator, the aim is to maximize the particle beam energy. Interactions with these environments can be costly or time-consuming, demanding decision-making systems to work in small-data regimes. Bayesian optimization (BO) is a powerful data- driven framework for global optimization that adaptively chooses actions to evaluate. Its potential for impactful real-world applications is vast, from those mentioned above to widespread automated machine learning (ML) services. There are, however, practical challenges that impede its implementation or result in sub-optimal decisions. This dissertation aims to advance the applicability of BO by addressing three cru- cial points: risk-aversion, which ensures performance beyond the average only; query- effectiveness, which aims at smart use of budgets covering evaluation costs; and problem- adaptiveness, which leverages the structure of the decision space. To this end, we propose novel approaches and examine them theoretically and empirically in real scenarios. First, we tackle balancing high utility and low risk – a serious issue in high-stakes applica- tions. For example, the accelerator’s maximum pulse energy must be stable to observe chem- ical reactions; or in drug discovery, the drug must succeed for all individuals. Our approach trades off mean and input-dependent aleatoric uncertainty (both learned on the fly during optimization) and provides theoretical sample complexity results. Moreover, our empirical study on tuning a particle accelerator and ML models shows the benefit of the approach. Second, we aim at efficient budget allocation, enriching the practical performance heavily dependent on the interaction cost and the available budget covering these costs. For example, the success of a timely drug discovery depends on the smart use of the resources at hand. We tackle two crucial questions of query efficiency in BO: (1) how to use cheaper but less accurate evaluations, and (2) when to stop the optimization. We leverage multi-fidelity optimization and incorporate the evaluation costs in a natural information-theoretic manner. Moreover, our automatic termination approach for the BO loop determines the minimal budget required for obtaining a high-quality solution. Finally, the complex and non-continuous nature of the decision variables can make applying Bayesian optimization in areas such as drug design or automated ML difficult. Our approach for mixed-variable BO exploits the structure and interconnections within the discrete subdomain, learning them on the fly during the optimization. Our approaches make BO applicable to a wider range of critical applications while combining practical simplicity with theoretically grounded reasoning.