# Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints

arXiv: https://arxiv.org/abs/2505.22881 · HTML: https://mlsanity.com/paper/2505.22881/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 53 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 30 of 36)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [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)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [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)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Generalization Bounds in the Predict-then-Optimize Framework](https://mlsanity.com/paper/1905.11488/) (2019)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Applying Deep Learning to the Newsvendor Problem](https://mlsanity.com/paper/1607.02177/) (2016)
- [Residuals-based distributionally robust optimization with covariate information](https://mlsanity.com/paper/2012.01088/) (2020)
- [Stochastic Optimization Forests](https://mlsanity.com/paper/2008.07473/) (2020)
- [Distributionally robust stochastic programs with side information based on trimmings -- Extended version](https://mlsanity.com/paper/2009.10592/) (2020)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [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)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Learning Decision-Focused Uncertainty Sets in Robust Optimization](https://mlsanity.com/paper/2305.19225/) (2023)
- [Bootstrap Robust Prescriptive Analytics](https://mlsanity.com/paper/1711.09974/) (2017)

## Built on by (most cited first, 2 of 2)

- [Decision-Focused Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)
- [Geometric Identification in Predict-Then-Optimize Learning](https://mlsanity.com/paper/2609.33472/) (2026)

## Abstract (arXiv)

We study an extension of contextual stochastic linear optimization (CSLO) that, in contrast to most of the existing literature, involves inequality constraints that depend on uncertain parameters predicted by a machine learning model. To handle the constraint uncertainty, we use contextual uncertainty sets constructed via methods like conformal prediction. Given a contextual uncertainty set method, we introduce the "Smart Predict-then-Optimize with Robust Constraints" (SPO-RC) loss, a feasibility-sensitive adaptation of the SPO loss that measures decision error of predicted objective parameters. We also introduce a convex surrogate, SPO-RC+, and prove Fisher consistency with SPO-RC. To enhance performance, we train on truncated datasets where true constraint parameters lie within the uncertainty sets, and we correct the induced sample selection bias using importance reweighting techniques. Through experiments on fractional knapsack and alloy production problem instances, we demonstrate that SPO-RC+ effectively handles uncertainty in constraints and that combining truncation with importance reweighting can further improve performance.