# Learning to Optimize with Stochastic Dominance Constraints

arXiv: https://arxiv.org/abs/2211.07767 · HTML: https://mlsanity.com/paper/2211.07767/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 14 Nov 2022.

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

- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods](https://mlsanity.com/paper/1902.08297/) (2019)
- [Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2006.10643/) (2020)
- [Optimizing the CVaR via Sampling](https://mlsanity.com/paper/1404.3862/) (2014)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Constrained Discrete Black-Box Optimization using Mixed-Integer Programming](https://mlsanity.com/paper/2110.09569/) (2021)
- [Neural Stochastic Dual Dynamic Programming](https://mlsanity.com/paper/2112.00874/) (2021)

## Built on by (most cited first, 5 of 5)

- [Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement](https://mlsanity.com/paper/2306.12803/) (2023)
- [Statistical Multicriteria Benchmarking via the GSD-Front](https://mlsanity.com/paper/2406.03924/) (2024)
- [Safe RLHF Beyond Expectation: Stochastic Dominance for Universal Spectral Risk Control](https://mlsanity.com/paper/2603.10938/) (2026)
- [Beyond Expectations: Learning with Stochastic Dominance Made Practical](https://mlsanity.com/paper/2402.02698/) (2024)
- [N(CO)2: Neural Combinatorial Optimization with Chance Constraints to Solve Stochastic Orienteering](https://mlsanity.com/paper/2606.18514/) (2026)

## Abstract (arXiv)

In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach for comparing uncertain quantities, but optimization with stochastic dominance constraints is often computationally expensive, which limits practical applicability. In this paper, we develop a simple yet efficient approach for the problem, the Light Stochastic Dominance Solver (light-SD), that leverages useful properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability and leads to tractable updates or even closed-form solutions for gradient calculations. We prove convergence of the algorithm and test it empirically. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.