Researchers prove convergence rates for OCE risk minimization algorithm

A team of researchers—Sumedh Gupte, Prashanth L. A., and Sanjay P. Bhat—has released a new paper on arXiv that tackles Optimized Certainty Equivalent (OCE) risk minimization, a general risk measure used across finance and machine learning. Their work unifies popular risk metrics like entropic risk, mean-variance risk, and smooth variants of Conditional Value-at-Risk (CVaR) under a single optimization framework. The authors establish conditions that extend OCE to unbounded random variables, making the theory applicable to real-world heavy-tailed data.

The key theoretical contribution is a characterization linking OCE to utility-based shortfall risk (UBSR). This connection lets them construct an OCE estimator directly from the classic sample-average approximation (SAA) of UBSR, for which they derive mean-squared error (MSE) bounds. Building on this, they compute an exact gradient expression for OCE and design a gradient estimator with provable non-asymptotic MSE guarantees. They then integrate this estimator into a stochastic gradient (SG) algorithm and quantify its convergence rate with non-asymptotic bounds, giving practitioners strong mathematical assurances when optimizing risk-sensitive objectives.

To demonstrate practical value, the authors run three experiments applying their OCE optimization algorithm to portfolio optimization and uncertainty quantification. These experiments show the method effectively balances risk and return while maintaining computational tractability. The paper is currently available as arXiv:2608.07113, and its code and additional resources are linked via standard arXiv tools. For machine learning engineers and quantitative researchers, this work provides a ready-to-use, theoretically grounded path to optimize risk measures without hand-tuning heuristics or worrying about convergence issues.