We consider the problem of estimating the Optimized Certainty Equivalent (OCE) risk from independent and identically distributed (i.i.d.) samples. For the classic sample average approximation (SAA) of OCE, we derive mean-squared error as well as concentration bounds (assuming sub-Gaussianity). Further, we analyze an efficient stochastic approximation-based OCE estimator, and derive finite sample bounds for the same. To show the applicability of our bounds, we consider a risk-aware bandit problem, with OCE as the risk. For this problem, we derive bound on the probability of mis-identification. Finally, we conduct numerical experiments to validate the theoretical findings.

翻译：我们考虑从独立同分布样本中估计优化确定性等价风险的问题。针对OCE的经典样本平均逼近方法，我们推导了均方误差以及集中界（假设次高斯性）。此外，我们分析了一种基于随机逼近的高效OCE估计器，并推导了其有限样本界。为展示所推导界的适用性，我们考虑了一个以OCE作为风险度量的风险感知赌博机问题。针对该问题，我们推导了误识别概率的界。最后，我们通过数值实验验证了理论结果。