# Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications

arXiv: https://arxiv.org/abs/2608.07113 · HTML: https://mlsanity.com/paper/2608.07113/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [A Wasserstein distance approach for concentration of empirical risk estimates](https://mlsanity.com/paper/1902.10709/) (2019)
- [Optimal Training of Mean Variance Estimation Neural Networks](https://mlsanity.com/paper/2302.08875/) (2023)
- [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)
- [Concentration Bounds for Optimized Certainty Equivalent Risk Estimation](https://mlsanity.com/paper/2405.20933/) (2024)
- [Multivariate Optimized Certainty Equivalent Risk Measures and their Numerical Computation](https://mlsanity.com/paper/2210.13825/) (2022)

## Built on by (most cited first, 1 of 1)

- [Conformal Risk-Averse Decision Making with Optimized Certainty Equivalent Risk Control](https://mlsanity.com/paper/2608.28179/) (2026)

## Abstract (arXiv)

We consider the optimization of the Optimized Certainty Equivalent (OCE) risk, with applications including portfolio optimization in finance, and uncertainty quantification, classification, and regression in machine learning. Our contributions cover popular special cases of OCE, such as entropic risk, mean-variance risk, and smooth variants of Conditional Value-at-Risk. Our treatment sets out the conditions that facilitate the extension of OCE to unbounded r.v.s.. We provide a useful characterization of OCE that links OCE to utility-based shortfall risk (UBSR). Our characterization enables us to form an OCE estimator from the classic sample-average approximation (SAA) of UBSR. We derive mean-squared error (MSE) bounds for our proposed OCE estimator. For OCE optimization, we first derive an expression for the OCE gradient using the characterization linking OCE to UBSR. This expression serves as the basis for a gradient estimator for the OCE. We derive non-asymptotic bounds on the MSE for the proposed OCE gradient estimator. We incorporate the aforementioned gradient estimator into a stochastic gradient (SG) algorithm to optimize OCE and quantify its convergence rate using non-asymptotic bounds that we derive. Finally, we present three experiments that use our OCE optimization algorithm to solve portfolio optimization and uncertainty quantification problems.