{"ID":2855089,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.13328","arxiv_id":"2510.13328","title":"Thompson Sampling via Fine-Tuning of LLMs","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. Within a collection of methods covering in-context Bayesian optimization, reinforcement learning, and evolutionary search, ToSFiT exhibits both state-of-the-art sample efficiency and computational efficiency.","short_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 parameteriz...","url_abs":"https://arxiv.org/abs/2510.13328","url_pdf":"https://arxiv.org/pdf/2510.13328v4","authors":"[\"Nicolas Menet\",\"Aleksandar Terzić\",\"Michael Hersche\",\"Andreas Krause\",\"Abbas Rahimi\"]","published":"2025-10-15T09:13:59Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Reinforcement Learning\",\"Large Language Model\",\"Language Model\"]","has_code":false}