Practical Bayesian Algorithm Execution via Posterior Sampling

Chu Xin Cheng, Raul Astudillo, Thomas Desautels, Yisong Yue

Keywords: Bayesian algorithm execution, Bayesian optimization, posterior sampling, probabilistic numerics

TL;DR: We propose a probabilistic framework to efficiently estimate a target set defined in terms of a function with expensive evaluations.

Abstract: We consider the Bayesian algorithm execution framework, where the goal is to select points for evaluating an expensive function to best infer a property of interest. By making the key observation that the property of interest for many tasks is a target set of points defined in terms of the function, we derive a simple yet effective and scalable posterior sampling algorithm, termed PS-BAX. Our approach addresses a broad range of problems, including many optimization variants and level-set estimation. Experiments across a diverse set of tasks show that PS-BAX achieves competitive performance against standard baselines, while being significantly faster, simpler to implement, and easily parallelizable. In addition, we show that PS-BAX is asymptotically consistent under mild regularity conditions. Consequently, our work yields new insights into posterior sampling, broadening its application scope and providing a strong baseline for future exploration.

Submission Number: 110