Maximizing acquisition functions for Bayesian optimization

TL;DR

This paper explores methods to effectively maximize acquisition functions in Bayesian optimization, demonstrating gradient-based optimization for Monte Carlo estimates and justifying greedy approaches for common functions like EI and UCB.

Contribution

It introduces gradient-based optimization techniques for Monte Carlo estimated acquisition functions and provides theoretical justification for greedy maximization of popular acquisition functions.

Findings

Gradient-based optimization effectively maximizes Monte Carlo estimated acquisition functions.

Greedy approaches are justified for maximizing common acquisition functions like EI and UCB.

The methods improve the efficiency of Bayesian optimization in high-dimensional, non-convex settings.

Abstract

Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functions produces the Bayes' decision rule, but this ideal is difficult to achieve since these functions are frequently non-trivial to optimize. This statement is especially true when evaluating queries in parallel, where acquisition functions are routinely non-convex, high-dimensional, and intractable. We first show that acquisition functions estimated via Monte Carlo integration are consistently amenable to gradient-based optimization. Subsequently, we identify a common family of acquisition functions, including EI and UCB, whose properties not only facilitate but justify use of greedy approaches for their maximization.