Thompson Sampling in Function Spaces via Neural Operators

Rafael Oliveira, Xuesong Wang, Kian Ming A. Chai, Edwin V. Bonilla

Keywords: neural operators, Thompson sampling, bandits, Bayesian optimization

TL;DR: An extension of Thompson sampling to optimization problems over function spaces using neural operators as surrogates

Abstract: We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that queries to the operator (such as running a high-fidelity simulator or physical experiment) are costly, while functional evaluations on the operator's output are inexpensive. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process (GP) posterior. We derive regret bounds and theoretical results connecting neural operators with GPs in infinite-dimensional settings. Experiments benchmark our method against other Bayesian optimization baselines on functional optimization tasks involving partial differential equations of physical systems, demonstrating better sample efficiency and significant performance gains.

Primary Area: General machine learning (supervised, unsupervised, online, active, etc.)

Submission Number: 26867