Concentration Bounds for Optimized Certainty Equivalent Risk Estimation

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.