Concentration Bounds for Optimized Certainty Equivalent Risk Estimation
<|reference_start|>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.<|reference_end|>
@article{ghosh2024concentration,
    title={Concentration Bounds for Optimized Certainty Equivalent Risk Estimation},
    author={Ayon Ghosh, L.A. Prashanth and Krishna Jagannathan},
    journal={arXiv preprint arXiv:2405.20933},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.20933},
    primaryClass={cs.LG stat.ML}
}