Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization

2026-04-10

AI Summary

This work addresses the challenge of high-dimensional Bayesian optimization, where conventional Thompson sampling suffers from exponentially sparse coverage due to its reliance on a fixed set of discrete candidate points, hindering effective approximation of the optimum. To overcome this limitation, the paper proposes Adaptive Candidate Thompson Sampling (ACTS), which innovatively leverages gradient information from samples of the Gaussian process surrogate model to dynamically refine the sampling subspace. This approach significantly enhances both sampling density and the quality of sampled maxima without increasing the number of candidate points. ACTS integrates seamlessly into existing Thompson sampling frameworks and demonstrates consistent superiority over state-of-the-art methods across multiple synthetic and real-world benchmarks, achieving notable improvements in both optimization efficiency and solution quality.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Bayesian optimization
• Thompson sampling
• high-dimensional
• candidate points
• posterior sampling

Innovation

• Thompson Sampling
• Bayesian Optimization
• Adaptive Candidate Points
• High-Dimensional Optimization
• Gaussian Process