MINTS: Minimalist Thompson Sampling

2026-06-01

AI Summary

This work addresses the inflexibility of traditional Bayesian sequential decision-making methods, which require full parametric modeling and struggle to incorporate structural constraints. The authors propose a minimalist Bayesian framework that places a prior only on the location of the optimal arm and leverages profile likelihood to eliminate nuisance parameters, yielding a generalized posterior that naturally accommodates structural assumptions such as unimodality. Building on this, they introduce the MINTS algorithm—the first to integrate minimalist Bayesian principles into Thompson sampling—enabling automatic adaptation to structural constraints without modeling irrelevant parameters while preserving theoretical optimality. In mean-constrained multi-armed bandits, MINTS achieves near-optimal non-asymptotic regret bounds; under no structure and unimodal settings, it attains the classic Lai–Robbins constant and a sharp asymptotic constant dependent solely on the neighborhood of the optimal arm, respectively.

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.

Problem

• Bayesian sequential decision-making
• structural constraints
• multi-armed bandits
• Thompson Sampling
• nuisance parameters

Innovation

• Minimalist Bayesian
• Thompson Sampling
• Profile Likelihood
• Structural Constraints
• Regret Optimality