Conditional value-at-risk (CVaR) and value-at-risk (VaR) are popular tail-risk measures in finance and insurance industries where often the underlying probability distributions are heavy-tailed. We use the multi-armed bandit best-arm identification framework and consider the problem of identifying the arm-distribution from amongst finitely many that has the smallest CVaR or VaR. We first show that in the special case of arm-distributions belonging to a single-parameter exponential family, both these problems are equivalent to the best mean-arm identification problem, which is widely studied in the literature. This equivalence however is not true in general. We then propose optimal $\delta$-correct algorithms that act on general arm-distributions, including heavy-tailed distributions, that match the lower bound on the expected number of samples needed, asymptotically (as $ \delta$ approaches $0$). En-route, we also develop new non-asymptotic concentration inequalities for certain functions of these risk measures for the empirical distribution, that may have wider applicability.

本论文提出了一种基于多臂赌博机算法的方法，用于识别在金融行业和不确定环境中具有最小条件风险价值、价值风险价值或条件风险价值加权平均的多臂赌博机，其主要贡献是一种能够适用于包括重尾分布在内的一般分布上的最优算法，匹配了样本所需的预期数量下界，同时开发了新的经验浓度不等式方法以提高估计精度。

基于尾风险度量的最优臂识别方法