Gaussian Process Thompson Sampling via Rootfinding

Fuente: arXiv
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Autori principali: Adebiyi, Taiwo A., Do, Bach, Zhang, Ruda
Natura: Preprint
Pubblicazione: 2024
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author Adebiyi, Taiwo A.
Do, Bach
Zhang, Ruda
author_facet Adebiyi, Taiwo A.
Do, Bach
Zhang, Ruda
contents Thompson sampling (TS) is a simple, effective stochastic policy in Bayesian decision making. It samples the posterior belief about the reward profile and optimizes the sample to obtain a candidate decision. In continuous optimization, the posterior of the objective function is often a Gaussian process (GP), whose sample paths have numerous local optima, making their global optimization challenging. In this work, we introduce an efficient global optimization strategy for GP-TS that carefully selects starting points for gradient-based multi-start optimizers. It identifies all local optima of the prior sample via univariate global rootfinding, and optimizes the posterior sample using a differentiable, decoupled representation. We demonstrate remarkable improvement in the global optimization of GP posterior samples, especially in high dimensions. This leads to dramatic improvements in the overall performance of Bayesian optimization using GP-TS acquisition functions, surprisingly outperforming alternatives like GP-UCB and EI.
format Preprint
id arxiv_https___arxiv_org_abs_2410_08071
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Gaussian Process Thompson Sampling via Rootfinding
Adebiyi, Taiwo A.
Do, Bach
Zhang, Ruda
Machine Learning
Optimization and Control
Thompson sampling (TS) is a simple, effective stochastic policy in Bayesian decision making. It samples the posterior belief about the reward profile and optimizes the sample to obtain a candidate decision. In continuous optimization, the posterior of the objective function is often a Gaussian process (GP), whose sample paths have numerous local optima, making their global optimization challenging. In this work, we introduce an efficient global optimization strategy for GP-TS that carefully selects starting points for gradient-based multi-start optimizers. It identifies all local optima of the prior sample via univariate global rootfinding, and optimizes the posterior sample using a differentiable, decoupled representation. We demonstrate remarkable improvement in the global optimization of GP posterior samples, especially in high dimensions. This leads to dramatic improvements in the overall performance of Bayesian optimization using GP-TS acquisition functions, surprisingly outperforming alternatives like GP-UCB and EI.
title Gaussian Process Thompson Sampling via Rootfinding
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2410.08071