论文标题
多臂匪徒中统计上强大的，规避风险的最佳手臂识别
Statistically Robust, Risk-Averse Best Arm Identification in Multi-Armed Bandits
论文作者
论文摘要
传统的多武器强盗（MAB）配方通常对基础武器的分布做出某些假设，例如支撑或尾部行为的界限。此外，此类参数信息通常被“烤制”到算法中。在本文中，我们表明，当参数被误指定时，利用此类参数信息的专门算法很容易出现学习性能。我们的主要贡献是双重的：（i）我们在固定预算的纯勘探环境下建立了统计上强大的mAb算法的基本性能限制，并且（ii）我们提出了两类渐近的算法，这些算法是近乎最佳的。此外，我们考虑了最佳手臂识别的风险感知标准，其中与每个ARM相关的目标是平均值的线性组合和有条件的风险（CVAR）。在整个过程中，我们做出了一个非常温和的“有限的力矩”假设，这使我们能够在统一框架内与轻尾和重尾分布一起工作。
Traditional multi-armed bandit (MAB) formulations usually make certain assumptions about the underlying arms' distributions, such as bounds on the support or their tail behaviour. Moreover, such parametric information is usually 'baked' into the algorithms. In this paper, we show that specialized algorithms that exploit such parametric information are prone to inconsistent learning performance when the parameter is misspecified. Our key contributions are twofold: (i) We establish fundamental performance limits of statistically robust MAB algorithms under the fixed-budget pure exploration setting, and (ii) We propose two classes of algorithms that are asymptotically near-optimal. Additionally, we consider a risk-aware criterion for best arm identification, where the objective associated with each arm is a linear combination of the mean and the conditional value at risk (CVaR). Throughout, we make a very mild 'bounded moment' assumption, which lets us work with both light-tailed and heavy-tailed distributions within a unified framework.
