Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization
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Abstract (arXiv)
Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is first trained via a measure of predictive accuracy, and then its predictions are used as input into an optimization algorithm which produces a decision. However, the loss function used to train the model may easily be misaligned with the end goal, which is to make the best decisions possible. Hand-tuning the loss function to align with optimization is a difficult and error-prone process (which is often skipped entirely). We focus on combinatorial optimization problems and introduce a general framework for decision-focused learning, where the machine learning model is directly trained in conjunction with the optimization algorithm to produce high-quality decisions. Technically, our contribution is a means of integrating common classes of discrete optimization problems into deep learning or other predictive models, which are typically trained via gradient descent. The main idea is to use a continuous relaxation of the discrete problem to propagate gradients through the optimization procedure. We instantiate this framework for two broad classes of combinatorial problems: linear programs and submodular maximization. Experimental results across a variety of domains show that decision-focused learning often leads to improved optimization performance compared to traditional methods. We find that standard measures of accuracy are not a reliable proxy for a predictive model's utility in optimization, and our method's ability to specify the true goal as the model's training objective yields substantial dividends across a range of decision problems.
Key facts. Cited by 220 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Sep 2018.
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Citing papers per year: 2021: 19; 2022: 33; 2023: 37; 2024: 40; 2025: 41; 2026: 50.
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- 2021DC3: A learning method for optimization with hard constraintscited by 181
- 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
- 2023Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunitiescited by 129
- 2021Implicit MLE: Backpropagating Through Discrete Exponential Family Distributionscited by 97
- 2023A Survey of Contextual Optimization Methods for Decision Making under Uncertaintycited by 81
- 2021Decision-Focused Learning: Through the Lens of Learning to Rankcited by 61
- 2024Learning Iterative Reasoning through Energy Diffusioncited by 36
- 2022PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programmingcited by 32
- 2022Learning Iterative Reasoning through Energy Minimizationcited by 32
- 2022Backpropagation through Combinatorial Algorithms: Identity with Projection Workscited by 29
- 2022Learning with Combinatorial Optimization Layers: a Probabilistic Approachcited by 28
- 2021Integrated Conditional Estimation-Optimizationcited by 25
38 more
- 2021Learning Hard Optimization Problems: A Data Generation Perspectivecited by 21
- 2022SurCo: Learning Linear Surrogates For Combinatorial Nonlinear Optimization Problemscited by 21
- 2022Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketingcited by 21
- 2021Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Methodcited by 20
- 2022End-to-End Stochastic Optimization with Energy-Based Modelcited by 19
- 2023Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspectivecited by 19
- 2023Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimizecited by 18
- 2025Gen-DFL: Decision-Focused Generative Learning for Robust Decision Makingcited by 18
- 2023Landscape Surrogate: Learning Decision Losses for Mathematical Optimization Under Partial Informationcited by 17
- 2024Decision-Focused Learning with Directional Gradientscited by 16
- 2024Mechanistic Neural Networks for Scientific Machine Learningcited by 16
- 2024Learning Constrained Optimization with Deep Augmented Lagrangian Methodscited by 16
- 2021The Perils of Learning Before Optimizingcited by 15
- 2021Learning Revenue-Maximizing Auctions With Differentiable Matchingcited by 14
- 2022Decision-Aware Learning for Optimizing Health Supply Chainscited by 14
- 2024End-to-End Conformal Calibration for Optimization Under Uncertaintycited by 14
- 2023Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programmingcited by 13
- 2023Backpropagation of Unrolled Solvers with Folded Optimizationcited by 13
- 2022Scalable Decision-Focused Learning in Restless Multi-Armed Bandits with Application to Maternal and Child Healthcited by 12
- 2022Decision-Focused Learning without Differentiable Optimization: Learning Locally Optimized Decision Lossescited by 12
- 2022Adaptive Perturbation-Based Gradient Estimation for Discrete Latent Variable Modelscited by 12
- 2022Predict+Optimize for Packing and Covering LPs with Unknown Parameters in Constraintscited by 11
- 2023Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splittingcited by 11
- 2023TaskMet: Task-Driven Metric Learning for Model Learningcited by 11
- 2024Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantificationcited by 11
- 2023Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learningcited by 10
- 2023Generalization Bound and Learning Methods for Data-Driven Projections in Linear Programmingcited by 10
- 2024First-Order Methods for Linearly Constrained Bilevel Optimizationcited by 10
- 2024End-to-End Cost-Effective Incentive Recommendation under Budget Constraint with Uplift Modelingcited by 10
- 2024BPQP: A Differentiable Convex Optimization Framework for Efficient End-to-End Learningcited by 10
- 2023A Unified View on Solving Objective Mismatch in Model-Based Reinforcement Learningcited by 9
- 2024Decision Focused Causal Learning for Direct Counterfactual Marketing Optimizationcited by 9
- 2023Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regimecited by 8
- 2024Differentiable Distributionally Robust Optimization Layerscited by 8
- 2024Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guaranteescited by 8
- 2025Solver-Free Decision-Focused Learning for Linear Optimization Problemscited by 8
- 2024GLinSAT: The General Linear Satisfiability Neural Network Layer By Accelerated Gradient Descentcited by 7
- 2025Revisiting Online Learning Approach to Inverse Linear Optimization: A Fenchel-Young Loss Perspective and Gap-Dependent Regret Analysiscited by 7
50 most cited of 220 All 220 (JSON)
- 2026The Curvature of Regret in Contextual Linear Optimization1 Oct 2026
- 2026When Evidence Changes the Subject: Subject-Typed Claim Licensing for Learned Routing27 Sep 2026
- 2026PolyStepOR: Learning to Decide Without Optimal Decisions26 Sep 2026
- 2026Entropy Regularization: A Free Correction to Cross-Entropy for Verified Demonstrations24 Sep 2026
- 2026The Operational Value of Spatial Dependence in Renewable Forecast Scenarios for Single-Period Economic Dispatch: A Controlled Ablation Study21 Sep 2026
- 2026Proximal Residual Value Functions for Consistent Planning and Real-Time Execution19 Sep 2026
- 2026Decision-Focused Learning for Mean-Variance Portfolio Optimization via KKT-Based Reformulation18 Sep 2026
- 2026Eigenvalue-Decomposition Cost Denoising as an Alternative to Predict-then-Optimize for Shortest-Path Problems14 Sep 2026
- 2026Decision-Oriented Uncertainty Quantification for Risk Control in Earth System Spatiotemporal Foundation Models13 Sep 2026
- 2026SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery12 Sep 2026
- 2026PruneShift: A Framework for Evaluating Decision Reliability in Structured Pruning30 Aug 2026
- 2026Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift29 Aug 2026
38 more
- 2026CEDAR: Controlled and Event-Driven Demand Forecasting via Residual Decomposition26 Aug 2026
- 2026Constrained Graph Diffusion for Mixed Integer Optimization13 Aug 2026
- 2026Control-Oriented Scenario Tree Construction through Reinforcement Learning10 Aug 2026
- 2026Decision-Focused Learning in Network Interdiction Games10 Aug 2026
- 2026Hard Constraints, Smooth Gradients: Learning Feasible Inventory Policies via Differentiable Projection3 Aug 2026
- 2026RankCert: When Can Simulated Learners Safely Select an AI Tutor? Robust Decision Certification Under Structural Uncertainty2 Aug 2026
- 2026End-to-End Fairness Optimization with Fair Decision-Focused Learning31 Jul 2026
- 2026Paired Exact-Reset Evaluation of a Prediction-Derived Medium-to-Full World-Model Cascade30 Jul 2026
- 2026Multi-channel Uplift Policy Learning30 Jul 2026
- 2026Smooth Learning with Hard Constraints via Legendre-Regularized Policies27 Jul 2026
- 2026Explicit Iteration Complexity of Exact Data-Driven Inverse Optimization for Integer Linear Programs24 Jul 2026
- 2026Breaking Feedback-Blindness: Utility-Augmented Transformer for Sequential Decision Making21 Jul 2026
- 2026Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimization10 Jul 2026
- 2026Decision-Aware Training for Sample-Based Generative Models1 Jul 2026
- 2026The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tails25 Jun 2026
- 2026DT2: Decision-Targeted Digital Twins24 Jun 2026
- 2026Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application24 Jun 2026
- 2026Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs19 Jun 2026
- 2026A Solver-Free Training Method for Predict-then-Optimize17 Jun 2026
- 2026Decision-Weighted Flow Matching for Contextual Stochastic Optimization15 Jun 2026
- 2026CloudCons: A Comprehensive End-to-End Benchmark for Cloud Resource Consolidation11 Jun 2026
- 2026Aligning Data-Driven Predictors with Allocation: A Decision-Focused Approach to Survival Analysis1 Jun 2026
- 2026DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers28 May 2026
- 2026Scalable Decision-Focused Learning through Cost-Sensitive Regression18 May 2026
- 2026PlantPose: Universal Plant Skeleton Estimation via Tree-constrained Graph Generation18 May 2026
- 2026Quantum End-to-End Learning for Contextual Combinatorial Optimization13 May 2026
- 2026Regret Equals Covariance: A Closed-Form Characterization for Stochastic Optimization13 May 2026
- 2026Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Sampling12 May 2026
- 2026IGT-OMD: Implicit Gradient Transport for Decision-Focused Learning under Delayed Feedback12 May 2026
- 2026Learning Polyhedral Conformal Sets for Robust Optimization8 May 2026
- 2026Decision-Focused Learning via Tangent-Space Projection of Prediction Error2 May 2026
- 2026Horizon-Constrained Rashomon Sets for Chaotic Forecasting17 Apr 2026
- 2026Loss-Driven Bayesian Active Learning13 Apr 2026
- 2026Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers13 Apr 2026
- 2026Decisions and Deployment: The Five-Year SAHELI Project (2020-2025) on Restless Multi-Armed Bandits for Improving Maternal and Child Health8 Apr 2026
- 2026Latent Spherical Flow Policy for Reinforcement Learning with Combinatorial Actions29 Jan 2026
- 2026Managing Solution Stability in Decision-Focused Learning with Cost Regularization29 Jan 2026
- 2026Learning Shortest Paths When Data is Scarce7 Jan 2026
50 newest of 220 All 220 (JSON)
- 2021DC3: A learning method for optimization with hard constraintscited by 181
- 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
- 2023Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunitiescited by 129
- 2021Implicit MLE: Backpropagating Through Discrete Exponential Family Distributionscited by 97
- 2023A Survey of Contextual Optimization Methods for Decision Making under Uncertaintycited by 81
- 2021Decision-Focused Learning: Through the Lens of Learning to Rankcited by 61
- 2024Learning Iterative Reasoning through Energy Diffusioncited by 36
- 2022PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programmingcited by 32
- 2022Learning Iterative Reasoning through Energy Minimizationcited by 32
- 2022Learning with Combinatorial Optimization Layers: a Probabilistic Approachcited by 28
- 2021Integrated Conditional Estimation-Optimizationcited by 25
- 2021Learning Hard Optimization Problems: A Data Generation Perspectivecited by 21
12 most cited of 212 All 212 (JSON)
- 2026The Curvature of Regret in Contextual Linear Optimization1 Oct 2026
- 2026When Evidence Changes the Subject: Subject-Typed Claim Licensing for Learned Routing27 Sep 2026
- 2026PolyStepOR: Learning to Decide Without Optimal Decisions26 Sep 2026
- 2026Entropy Regularization: A Free Correction to Cross-Entropy for Verified Demonstrations24 Sep 2026
- 2026The Operational Value of Spatial Dependence in Renewable Forecast Scenarios for Single-Period Economic Dispatch: A Controlled Ablation Study21 Sep 2026
- 2026Proximal Residual Value Functions for Consistent Planning and Real-Time Execution19 Sep 2026
- 2026Decision-Focused Learning for Mean-Variance Portfolio Optimization via KKT-Based Reformulation18 Sep 2026
- 2026Eigenvalue-Decomposition Cost Denoising as an Alternative to Predict-then-Optimize for Shortest-Path Problems14 Sep 2026
- 2026Decision-Oriented Uncertainty Quantification for Risk Control in Earth System Spatiotemporal Foundation Models13 Sep 2026
- 2026SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery12 Sep 2026
- 2026PruneShift: A Framework for Evaluating Decision Reliability in Structured Pruning30 Aug 2026
- 2026Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift29 Aug 2026
12 newest of 212 All 212 (JSON)