# Differentiable Distributionally Robust Optimization Layers

arXiv: https://arxiv.org/abs/2406.16571 · HTML: https://mlsanity.com/paper/2406.16571/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Builds on (most cited first, 26 of 26)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [Learning with Combinatorial Optimization Layers: a Probabilistic Approach](https://mlsanity.com/paper/2207.13513/) (2022)
- [Solution Refinement at Regular Points of Conic Problems](https://mlsanity.com/paper/1811.02157/) (2018)
- [Stochastic Optimization Forests](https://mlsanity.com/paper/2008.07473/) (2020)
- [End-to-End Stochastic Optimization with Energy-Based Model](https://mlsanity.com/paper/2211.13837/) (2022)
- [Landscape Surrogate: Learning Decision Losses for Mathematical Optimization Under Partial Information](https://mlsanity.com/paper/2307.08964/) (2023)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [Predict-then-Calibrate: A New Perspective of Robust Contextual LP](https://mlsanity.com/paper/2305.15686/) (2023)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming](https://mlsanity.com/paper/1904.01934/) (2019)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)

## Built on by (most cited first, 8 of 8)

- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Distributionally Robust Optimization via Diffusion Ambiguity Modeling](https://mlsanity.com/paper/2510.22757/) (2025)
- [Distributionally Robust Optimization via Generative Ambiguity Modeling](https://mlsanity.com/paper/2602.08976/) (2026)
- [Robust Generalization with Adaptive Optimal Transport Priors for Decision-Focused Learning](https://mlsanity.com/paper/2602.01427/) (2026)
- [SALD: Self-Referenced Advantage Learning for Diffusion Models](https://mlsanity.com/paper/2610.01496/) (2026)
- [3D-Learning: Diffusion-Augmented Distributionally Robust Decision-Focused Learning](https://mlsanity.com/paper/2602.02943/) (2026)
- [Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption](https://mlsanity.com/paper/2605.30089/) (2026)
- [Generative Distributionally Robust Optimization](https://mlsanity.com/paper/2607.24983/) (2026)

## Abstract (arXiv)

In recent years, there has been a growing research interest in decision-focused learning, which embeds optimization problems as a layer in learning pipelines and demonstrates a superior performance than the prediction-focused approach. However, for distributionally robust optimization (DRO), a popular paradigm for decision-making under uncertainty, it is still unknown how to embed it as a layer, i.e., how to differentiate decisions with respect to an ambiguity set. In this paper, we develop such differentiable DRO layers for generic mixed-integer DRO problems with parameterized second-order conic ambiguity sets and discuss its extension to Wasserstein ambiguity sets. To differentiate the mixed-integer decisions, we propose a novel dual-view methodology by handling continuous and discrete parts of decisions via different principles. Specifically, we construct a differentiable energy-based surrogate to implement the dual-view methodology and use importance sampling to estimate its gradient. We further prove that such a surrogate enjoys the asymptotic convergency under regularization. As an application of the proposed differentiable DRO layers, we develop a novel decision-focused learning pipeline for contextual distributionally robust decision-making tasks and compare it with the prediction-focused approach in experiments.