# A Survey of Contextual Optimization Methods for Decision Making under Uncertainty

arXiv: https://arxiv.org/abs/2306.10374 · HTML: https://mlsanity.com/paper/2306.10374/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- Builds on 88 of its 189 references that are in the map.
- First posted on arXiv 17 Jun 2023.

## Builds on (most cited first, 30 of 88)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [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)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [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)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [The Value Equivalence Principle for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2011.03506/) (2020)
- [Generalized Inner Loop Meta-Learning](https://mlsanity.com/paper/1910.01727/) (2019)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Learning with Differentiable Perturbed Optimizers](https://mlsanity.com/paper/2002.08676/) (2020)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [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)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)

## Built on by (most cited first, 30 of 82)

- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [Decision-Focused Learning with Directional Gradients](https://mlsanity.com/paper/2402.03256/) (2024)
- [Contextual Stochastic Bilevel Optimization](https://mlsanity.com/paper/2310.18535/) (2023)
- [Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantification](https://mlsanity.com/paper/2410.01767/) (2024)
- [Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning](https://mlsanity.com/paper/2307.05213/) (2023)
- [TaskMet: Task-Driven Metric Learning for Model Learning](https://mlsanity.com/paper/2312.05250/) (2023)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [What Data Enables Optimal Decisions? An Exact Characterization for Linear Optimization](https://mlsanity.com/paper/2505.21692/) (2025)
- [CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs](https://mlsanity.com/paper/2312.07718/) (2023)
- [Differentiable Distributionally Robust Optimization Layers](https://mlsanity.com/paper/2406.16571/) (2024)
- [Towards a Systems Theory of Algorithms](https://mlsanity.com/paper/2401.14029/) (2024)
- [Structured Reinforcement Learning for Combinatorial Decision-Making](https://mlsanity.com/paper/2505.19053/) (2025)
- [Robust Losses for Decision-Focused Learning](https://mlsanity.com/paper/2310.04328/) (2023)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [A Functional Model Method for Nonconvex Nonsmooth Conditional Stochastic Optimization](https://mlsanity.com/paper/2405.10815/) (2024)
- [Primal-dual algorithm for contextual stochastic combinatorial optimization](https://mlsanity.com/paper/2505.04757/) (2025)
- [Online Decision-Focused Learning](https://mlsanity.com/paper/2505.13564/) (2025)
- [Decision-Focused Learning via Tangent-Space Projection of Prediction Error](https://mlsanity.com/paper/2605.01361/) (2026)
- [Regret Equals Covariance: A Closed-Form Characterization for Stochastic Optimization](https://mlsanity.com/paper/2605.14019/) (2026)
- [Learning Lagrangian Multipliers for the Travelling Salesman Problem](https://mlsanity.com/paper/2312.14836/) (2023)
- [Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems](https://mlsanity.com/paper/2407.17200/) (2024)
- [Regularization for Adversarial Robust Learning](https://mlsanity.com/paper/2408.09672/) (2024)
- [Combinatorial Optimization Augmented Machine Learning](https://mlsanity.com/paper/2601.10583/) (2026)
- [A Solver-Free Training Method for Predict-then-Optimize](https://mlsanity.com/paper/2606.19587/) (2026)
- [Forecasting Outside the Box: Application-Driven Optimal Pointwise Forecasts for Stochastic Optimization](https://mlsanity.com/paper/2411.03520/) (2024)
- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)
- [Learning with Local Search MCMC Layers](https://mlsanity.com/paper/2505.14240/) (2025)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)

## Abstract (arXiv)

Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty. This gave rise to the field of contextual optimization, under which data-driven procedures are developed to prescribe actions to the decision-maker that make the best use of the most recently updated information. A large variety of models and methods have been presented in both OR and ML literature under a variety of names, including data-driven optimization, prescriptive optimization, predictive stochastic programming, policy optimization, (smart) predict/estimate-then-optimize, decision-focused learning, (task-based) end-to-end learning/forecasting/optimization, etc. Focusing on single and two-stage stochastic programming problems, this review article identifies three main frameworks for learning policies from data and discusses their strengths and limitations. We present the existing models and methods under a uniform notation and terminology and classify them according to the three main frameworks identified. Our objective with this survey is to both strengthen the general understanding of this active field of research and stimulate further theoretical and algorithmic advancements in integrating ML and stochastic programming.