MINTS: Minimalist Thompson Sampling

Two papers on sequential decision-making under uncertainty were submitted to arXiv in June 2026, introducing a minimalist Bayesian framework and analyzing Thompson sampling in stochastic generalised linear bandits.

The first paper, submitted on June 1, 2026^[1], presents MINimalist Thompson Sampling (MINTS), a Bayesian framework that places a prior only on the location of the optimum. MINTS eliminates nuisance parameters through profile likelihood, yielding a generalized posterior that accommodates structural constraints. The authors establish near-optimal non-asymptotic regret guarantees and sharp almost-sure asymptotic regret characterizations for multi-armed bandits with mean constraints. MINTS attains the classical Lai--Robbins constant in the unstructured setting and adapts to unimodal structure, achieving a sharp constant determined by the immediate neighbors of the optimal arm. A second paper, submitted on May 29, 2026^[2], examines Thompson sampling in stochastic generalised linear bandits, assuming a warm-up to control regret through the Gaussian Poincaré inequality. The authors note that previous optimism-based analyses break down at a certain point.