Batch Bayesian Optimization via Particle Gradient Flows

TL;DR

This paper introduces a novel batch Bayesian optimization method that reformulates the problem as an optimization over probability measures, utilizing gradient flows to efficiently solve the acquisition function optimization.

Contribution

It proposes a convex multipoint expected improvement acquisition function and gradient flow-based algorithms for batch Bayesian optimization, improving efficiency and effectiveness.

Findings

Outperforms existing batch BO methods on benchmark functions.

Demonstrates convexity of the new acquisition function over probability measures.

Provides practical gradient flow algorithms for inner optimization.

Abstract

Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the uncertainty in that surrogate through Bayesian inference. Objective evaluations are sequentially determined by maximising an acquisition function at each step. However, this ancilliary optimisation problem can be highly non-trivial to solve, due to the non-convexity of the acquisition function, particularly in the case of batch Bayesian optimisation, where multiple points are selected in every step. In this work we reformulate batch BO as an optimisation problem over the space of probability measures. We construct a new acquisition function based on multipoint expected improvement which is convex over the space of probability measures. Practical schemes for solving this `inner' optimisation problem arise naturally as gradient flows of this objective function. We demonstrate the efficacy of this new method on different benchmark functions and compare with state-of-the-art batch BO methods.