Thompson Sampling via Fine-Tuning of LLMs

• URL: http://arxiv.org/abs/2510.13328v2
• Date: Thu, 16 Oct 2025 08:38:06 GMT
• Title: Thompson Sampling via Fine-Tuning of LLMs
• Authors: Nicolas Menet, Aleksandar Terzić, Michael Hersche, Andreas Krause, Abbas Rahimi,
• Abstract summary: We propose an alternative based on Thompson sampling that eliminates the need for scalable large acquisition functions.<n>Our approach Thompson Sampling via Finening (ToSFiT) leverages the prior knowledge embedded in prompt-conditioned language models, and adapts incrementally toward the posterior.<n>Our analysis reveals the critical role of careful adaptation to the posterior probability of maximality-a principle that underpins our ToSFiT algorithm.
• Score: 68.1722422968855
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bayesian optimization in large unstructured discrete spaces is often hindered by the computational cost of maximizing acquisition functions due to the absence of gradients. We propose a scalable alternative based on Thompson sampling that eliminates the need for acquisition function maximization by directly parameterizing the probability that a candidate yields the maximum reward. Our approach, Thompson Sampling via Fine-Tuning (ToSFiT) leverages the prior knowledge embedded in prompt-conditioned large language models, and incrementally adapts them toward the posterior. Theoretically, we derive a novel regret bound for a variational formulation of Thompson Sampling that matches the strong guarantees of its standard counterpart. Our analysis reveals the critical role of careful adaptation to the posterior probability of maximality--a principle that underpins our ToSFiT algorithm. Empirically, we validate our method on three diverse tasks: FAQ response refinement, thermally stable protein search, and quantum circuit design. We demonstrate that online fine-tuning significantly improves sample efficiency, with negligible impact on computational efficiency.

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