Multi-Step Bayesian Optimization for One-Dimensional Feasibility Determination

TL;DR

This paper develops an efficient Bayes-optimal multi-step Bayesian optimization method for determining the superlevel set of a one-dimensional function, showing that one-step lookahead policies are nearly optimal in this context.

Contribution

It introduces a specialized approach for computing the Bayes-optimal policy in a one-dimensional setting with a Markov prior, and analyzes the suboptimality of one-step lookahead policies.

Findings

One-step lookahead policy achieves within 98% of optimal performance.

Efficient computation of Bayes-optimal policies for the specific problem.

Demonstrates near-optimality of simple policies in a specialized Bayesian optimization setting.

Abstract

Bayesian optimization methods allocate limited sampling budgets to maximize expensive-to-evaluate functions. One-step-lookahead policies are often used, but computing optimal multi-step-lookahead policies remains a challenge. We consider a specialized Bayesian optimization problem: finding the superlevel set of an expensive one-dimensional function, with a Markov process prior. We compute the Bayes-optimal sampling policy efficiently, and characterize the suboptimality of one-step lookahead. Our numerical experiments demonstrate that the one-step lookahead policy is close to optimal in this problem, performing within 98% of optimal in the experimental settings considered.