{"ID":2921205,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-04T00:54:56.190393508Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01655","arxiv_id":"2606.01655","title":"MINTS: Minimalist Thompson Sampling","abstract":"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. 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.","short_abstract":"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 optimu...","url_abs":"https://arxiv.org/abs/2606.01655","url_pdf":"https://arxiv.org/pdf/2606.01655v1","authors":"[\"Kaizheng Wang\"]","published":"2026-06-01T04:08:05Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.AI\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}