只对关键参数建模，用简化方法解决带约束的随机优化问题。
A Minimalist Bayesian Framework for Stochastic Optimization
- 仅对目标部分设先验，通过轮廓似然消除无关参数
- 算法在多臂老虎机上实现近最优后悔界
- 适合有复杂结构约束的优化场景
贝叶斯范式为不确定性下的序贯决策提供了严谨工具，但其对所有参数依赖概率模型的特性，会阻碍复杂结构约束的融入。本文提出一种极简贝叶斯框架，仅对关注的变量（如最优位置）设置先验，通过轮廓似然消除干扰参数，自然处理约束。作为实例，我们设计了极简汤普森采样（MINTS）算法。该框架适用于结构化问题，如连续动作空间的利普希茨老虎机和动态定价。同时，它为经典凸优化算法（如重心法、椭球法）提供了概率视角。我们进一步分析了MINTS在多臂老虎机上的表现，并建立了近最优的后悔率保证。
原文摘要 · Abstract (English)
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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