用汤普森采样找最优选项，同时满足随机约束条件。
Stochastically Constrained Best Arm Identification with Thompson Sampling
- 基于汤普森采样设计新算法，兼顾多目标优化与约束
- 理论证明后验收敛速率渐近最优
- 数值实验显示性能优于传统方法，适合多目标决策场景
我们研究在存在随机约束条件下寻找最优臂的问题，即多个臂对应多个性能指标，目标是在满足其余指标约束的前提下，找到使目标指标最优的臂。本文首次尝试将广受欢迎的汤普森采样（Thompson Sampling, TS）扩展到该问题。我们设计了一种基于TS的采样算法，建立了其在后验收敛速率上的渐近最优性，并通过数值实验验证了该方法的优越性能。
原文摘要 · Abstract (English)
We consider the problem of the best arm identification in the presence of stochastic constraints, where there is a finite number of arms associated with multiple performance measures. The goal is to identify the arm that optimizes the objective measure subject to constraints on the remaining measures. We will explore the popular idea of Thompson sampling (TS) as a means to solve it. To the best of our knowledge, it is the first attempt to extend TS to this problem. We will design a TS-based sampling algorithm, establish its asymptotic optimality in the rate of posterior convergence, and demonstrate its superior performance using numerical examples.
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