Efficient Rollout Strategies for Bayesian Optimization

TL;DR

This paper introduces efficient methods for implementing rollout strategies in Bayesian optimization, reducing computational costs and proposing a policy-search approach to improve optimization over complex, multi-modal functions.

Contribution

It combines quasi-Monte Carlo, common random numbers, and control variates to make rollout acquisition functions computationally feasible and introduces a policy-search method to bypass direct optimization.

Findings

Significant reduction in rollout computation time

Effective policy-search approach for Bayesian optimization

Insights into rollout policies for multi-modal objectives

Abstract

Bayesian optimization (BO) is a class of sample-efficient global optimization methods, where a probabilistic model conditioned on previous observations is used to determine future evaluations via the optimization of an acquisition function. Most acquisition functions are myopic, meaning that they only consider the impact of the next function evaluation. Non-myopic acquisition functions consider the impact of the next $h$ function evaluations and are typically computed through rollout, in which $h$ steps of BO are simulated. These rollout acquisition functions are defined as $h$-dimensional integrals, and are expensive to compute and optimize. We show that a combination of quasi-Monte Carlo, common random numbers, and control variates significantly reduce the computational burden of rollout. We then formulate a policy-search based approach that removes the need to optimize the rollout acquisition function. Finally, we discuss the qualitative behavior of rollout policies in the setting of multi-modal objectives and model error.