Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization

TL;DR

This paper introduces Adaptive Candidate Thompson Sampling (ACTS), a method that adaptively reduces the search space in high-dimensional Bayesian optimization to generate better candidate points and improve optimization performance.

Contribution

The paper proposes ACTS, an adaptive approach that enhances candidate point density by reducing the search space guided by surrogate model gradients, improving over existing Thompson sampling methods.

Findings

ACTS produces better samples of maxima in benchmarks.

ACTS improves optimization performance on synthetic and real-world problems.

ACTS is a simple drop-in replacement for existing Thompson sampling methods.

Abstract

In Bayesian optimization, Thompson sampling selects the evaluation point by sampling from the posterior distribution over the objective function maximizer. Because this sampling problem is intractable for Gaussian process (GP) surrogates, the posterior distribution is typically restricted to fixed discretizations (i.e., candidate points) that become exponentially sparse as dimensionality increases. While previous works aim to increase candidate point density through scalable GP approximations, our orthogonal approach increases density by adaptively reducing the search space during sampling. Specifically, we introduce Adaptive Candidate Thompson Sampling (ACTS), which generates candidate points in subspaces guided by the gradient of a surrogate model sample. ACTS is a simple drop-in replacement for existing TS methods -- including those that use trust regions or other local approximations -- producing better samples of maxima and improved optimization across synthetic and real-world benchmarks.