# Concentration Bounds for Optimized Certainty Equivalent Risk Estimation

arXiv: https://arxiv.org/abs/2405.20933 · HTML: https://mlsanity.com/paper/2405.20933/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 9 of 9)

- [Cumulative Prospect Theory Meets Reinforcement Learning: Prediction and Control](https://mlsanity.com/paper/1506.02632/) (2015)
- [Learning Bounds for Risk-sensitive Learning](https://mlsanity.com/paper/2006.08138/) (2020)
- [Distribution oblivious, risk-aware algorithms for multi-armed bandits with unbounded rewards](https://mlsanity.com/paper/1906.00569/) (2019)
- [A Wasserstein distance approach for concentration of empirical risk estimates](https://mlsanity.com/paper/1902.10709/) (2019)
- [Concentration bounds for temporal difference learning with linear function approximation: The case of batch data and uniform sampling](https://mlsanity.com/paper/1306.2557/) (2013)
- [PAC-Bayesian Bound for the Conditional Value at Risk](https://mlsanity.com/paper/2006.14763/) (2020)
- [Estimation of Spectral Risk Measures](https://mlsanity.com/paper/1912.10398/) (2019)
- [Online Estimation and Optimization of Utility-Based Shortfall Risk](https://mlsanity.com/paper/2111.08805/) (2021)
- [Optimization of utility-based shortfall risk: A non-asymptotic viewpoint](https://mlsanity.com/paper/2310.18743/) (2023)

## Built on by (most cited first, 2 of 2)

- [Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications](https://mlsanity.com/paper/2608.07113/) (2026)
- [Reinforcement learning with an expectile-based objective](https://mlsanity.com/paper/2602.09300/) (2026)

## Abstract (arXiv)

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.