A Minimalist Bayesian Framework for Stochastic Optimization

• URL: http://arxiv.org/abs/2509.07030v2
• Date: Wed, 08 Oct 2025 01:52:40 GMT
• Title: A Minimalist Bayesian Framework for Stochastic Optimization
• Authors: Kaizheng Wang,
• Abstract summary: We introduce a minimalist Bayesian framework that places a prior only on the component of interest, such as the location of the optimum.<n>As a direct instantiation, we develop a MINimalist Thompson Sampling (MINTS) algorithm.<n>It accommodates structured problems, including continuum-armed Lipschitz bandits and dynamic pricing.
• Score: 4.907205095294477
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 component of interest, such as the location of the optimum. Nuisance parameters are eliminated via profile likelihood, which naturally handles constraints. As a direct instantiation, we develop a MINimalist Thompson Sampling (MINTS) algorithm. Our framework accommodates structured problems, including continuum-armed Lipschitz bandits and dynamic pricing. It also provides a probabilistic lens on classical convex optimization algorithms such as the center of gravity and ellipsoid methods. We further analyze MINTS for multi-armed bandits and establish near-optimal regret guarantees.

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