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We introduce a minimalist Bayesian framework that places a prior only on the location of the optimum, while eliminating nuisance parameters through profile likelihood. This yields a generalized posterior that naturally accommodates structural constraints. As a direct instantiation, we develop MINimalist Thompson Sampling (MINTS). For multi-armed bandits with mean constraints, we establish near-optimal non-asymptotic regret guarantees and sharp almost-sure asymptotic regret characterizations. In particular, MINTS attains the classical Lai--Robbins constant in the unstructured setting and automatically adapts to unimodal structure, achieving the sharp constant determined only by the immediate neighbors of the optimal arm","title":"MINTS: Minimalist Thompson Sampling","url":"https://arxiv.org/abs/2606.01655","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.01655v1 Announce Type: cross \nAbstract: The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the location of the optimum, while eliminating nuisance parameters through profile likelihood. This yields a generalized posterior that naturally accommodates structural constraints. As a direct instantiation, we develop MINimalist Thompson Sampling (MINTS). For multi-armed bandits with mean constraints, we establish near-optimal non-asymptotic regret guarantees and sharp almost-sure asymptotic regret characterizations. 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