Concentration Bounds for Optimized Certainty Equivalent Risk Estimation
Ayon Ghosh, L. A. Prashanth, Krishna Jagannathan
TL;DR
This work develops nonasymptotic guarantees for estimating Optimized Certainty Equivalent (OCE) risk from i.i.d. losses. It introduces a batch sample-average estimator with mean-squared-error and concentration bounds under sub-Gaussian assumptions, and a streaming stochastic-approximation estimator with finite-sample guarantees, tailored for sequential data. The authors apply these results to risk-aware bandits, yielding a mis-identification bound, and validate both approaches through simulations in synthetic and credit-risk settings. Overall, the paper advances practical, nonasymptotic tools for OCE risk estimation across batch and streaming regimes with concrete performance guarantees.
Abstract
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.