# Beyond Expectations: Learning with Stochastic Dominance Made Practical

arXiv: https://arxiv.org/abs/2402.02698 · HTML: https://mlsanity.com/paper/2402.02698/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Optimizing the CVaR via Sampling](https://mlsanity.com/paper/1404.3862/) (2014)
- [Statistical Comparisons of Classifiers by Generalized Stochastic Dominance](https://mlsanity.com/paper/2209.01857/) (2022)
- [Stochastically Dominant Distributional Reinforcement Learning](https://mlsanity.com/paper/1905.07318/) (2019)
- [Learning to Optimize with Stochastic Dominance Constraints](https://mlsanity.com/paper/2211.07767/) (2022)
- [Introduction to Nonsmooth Analysis and Optimization](https://mlsanity.com/paper/2001.00216/) (2020)

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

- [Safe RLHF Beyond Expectation: Stochastic Dominance for Universal Spectral Risk Control](https://mlsanity.com/paper/2603.10938/) (2026)

## Abstract (arXiv)

Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying uncertainty, in contrast to simply resorting to the expectations. Despite theoretical appeal, the application of stochastic dominance in machine learning has been scarce, due to the following challenges: i), the original concept of stochastic dominance only provides a textitpartial order, and therefore, is not amenable to serve as a general optimality criterion; and ii), an efficient computational recipe remains lacking due to the continuum nature of evaluating stochastic dominance. In this work, we make the first attempt towards establishing a general framework of learning with stochastic dominance. We first generalize the stochastic dominance concept to enable feasible comparisons between any arbitrary pair of random variables. We next develop a simple and computationally efficient approach for finding the optimal solution in terms of stochastic dominance, which can be seamlessly plugged into many learning tasks. Numerical experiments demonstrate that the proposed method achieves comparable performance as standard risk-neutral strategies and obtains better trade-offs against risk across a variety of applications including supervised learning, reinforcement learning, and portfolio optimization.