基于混合与回收观测样本的优势臂识别

中文摘要 AI 辅助

我们研究多臂老虎机中的优势臂识别问题，目标是找到其奖励超过所有其他动作实际奖励概率最高的动作。传统基于均值和成对比较的算法常无法识别具有最高实际奖励的臂。为应对这一挑战，我们提出一种新的优势臂准则及具有理论保证的高效估计器。我们的方法依赖两项关键技术创新：（i）优势得分准则，即某一臂在划分后的奖励空间中击败局部优势臂；（ii）联合混合与回收机制，结合双重鲁棒估计器，保证所有臂的经验分布函数同时收敛。这些创新为高效计算全局臂优势提供了可能。我们提出的消除算法以近最优样本复杂度速率识别最佳优势臂。数值实验表明，我们的算法始终能准确恢复真实优势臂，性能优于现有基线方法。

英文摘要

We study the problem of identifying the dominant arm in multi-armed bandits, where the objective is to find the action with the highest probability of exceeding the realized rewards of all other actions. Conventional mean-based and pairwise comparison-based algorithms often fail to identify the arm with the highest realized reward. To address this challenge, we introduce a novel dominant arm criterion and an efficient estimator with theoretical guarantees. Our approach relies on two key technical innovations: (i) a dominance score criterion that an arm beats the locally dominant over the partitioned reward space and (ii) a joint mixing and recycling mechanism coupled with a doubly robust estimator that guarantees simultaneous convergence of the empirical distribution functions for all arms. These key innovations pave a way to efficient computation of global arm dominance. Our proposed elimination algorithm identifies the best dominant arm with nearly optimal rate of sample complexity. Numerical experiments demonstrate that our algorithm consistently achieves exact recovery of the true dominant arm, outperforming existing baselines.

发表机构

• Chung-Ang University（中央大学）

机构由 AI 辅助整理，请以论文原文为准。