MESHA：用于策略性线性博弈的机制强化序贯减半算法

中文摘要 AI 辅助

我们设计并分析了机制强化序贯减半算法（MESHA），这是一种用于策略性线性博弈中最佳臂识别（BAI）的算法。在此场景下，当奖励由各臂真实但不可观测的特征生成时，各臂可能会策略性地误报其特征向量，以最大化被识别为最佳臂的概率。MESHA的设计采用了朴素均匀采样规则和逐轮严厉触发条件（GTC）：前者减少臂的策略行为影响，后者消除那些报告特征严重偏离真实情况的臂。考虑任意纳什均衡，我们证明任何臂都会试图通过GTC检查以最大化其被识别概率，并得出MESHA在固定预算\(T\)内失败概率的上界。我们还表明，具有\(G\)最优设计的现有线性BAI算法在这种策略环境中会失败，因为基于策略性报告特征的基于最优设计（OD）的采样规则可能会使最优臂得不到任何采样预算。最后，大量数值实验表明MESHA优于依赖基于OD采样规则的基线以及与特征无关的基线，证实了MESHA的有效性。

英文摘要

We design and analyze \underline{M}echanism-\underline{E}nforced \underline{S}equential \underline{HA}lving (MESHA), an algorithm for Best Arm Identification (BAI) in strategic linear bandits. In this setting, each arm may strategically misreport its feature vector to maximize the probability of being identified as the best arm, when rewards are generated from the arms' true but unobservable features. The design of MESHA applies the naïve uniform sampling rule and an epoch-wise Grim Trigger Condition (GTC): the former reduces the impact of arms' strategic behaviours and the latter eliminates arms whose reported features severely deviate from the ground truth. Considering an arbitrary Nash Equilibrium, we prove that any arm would attempt to pass the GTC check to maximize its identified probability and derive an upper bound on the failure probability of MESHA within a fixed budget $T$. We also show that state-of-the-art linear BAI algorithms with $G$-optimal design would fail in such strategic environment, as the optimal design (OD)-based sampling rule based on strategically reported features may {\it starve} the optimal arm of any sampling budget. Finally, extensive numerical experiments indicate that MESHA outperforms baselines that rely on OD-based sampling rules as well as the feature-agnostic baselines, corroborating the efficacy of MESHA.

发表机构

• Data Science and Analytics Thrust, Hong Kong University of Science and Technology (Guangzhou)（数据科学与分析方向，香港科技大学（广州））

机构由 AI 辅助整理，请以论文原文为准。