Thompson Sampling in Function Spaces via Neural Operators

• URL: http://arxiv.org/abs/2506.21894v1
• Date: Fri, 27 Jun 2025 04:21:57 GMT
• Title: Thompson Sampling in Function Spaces via Neural Operators
• Authors: Rafael Oliveira, Xuesong Wang, Kian Ming A. Chai, Edwin V. Bonilla,
• Abstract summary: 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.<n>Our algorithm employs a sample-then-optimize approach using neural operator surrogates.
• Score: 14.0301500809197
• License: http://creativecommons.org/licenses/by/4.0/
• 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 functional evaluations are inexpensive, while queries to the operator (such as running a high-fidelity simulator) are costly. 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. We provide novel theoretical convergence guarantees, based on Gaussian processes in the infinite-dimensional setting, under minimal assumptions. We benchmark our method against existing baselines on functional optimization tasks involving partial differential equations and other nonlinear operator-driven phenomena, demonstrating improved sample efficiency and competitive performance.

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