# Decision-Focused Learning: Through the Lens of Learning to Rank

arXiv: https://arxiv.org/abs/2112.03609 · HTML: https://mlsanity.com/paper/2112.03609/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 7 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [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)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [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)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [End-to-end Learning for Fair Ranking Systems](https://mlsanity.com/paper/2111.10723/) (2021)

## Built on by (most cited first, 30 of 62)

- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Learning with Combinatorial Optimization Layers: a Probabilistic Approach](https://mlsanity.com/paper/2207.13513/) (2022)
- [Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketing](https://mlsanity.com/paper/2211.15728/) (2022)
- [Landscape Surrogate: Learning Decision Losses for Mathematical Optimization Under Partial Information](https://mlsanity.com/paper/2307.08964/) (2023)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Controlling Continuous Relaxation for Combinatorial Optimization](https://mlsanity.com/paper/2309.16965/) (2023)
- [Offline Model-Based Optimization by Learning to Rank](https://mlsanity.com/paper/2410.11502/) (2024)
- [Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning](https://mlsanity.com/paper/2307.05213/) (2023)
- [Decision Focused Causal Learning for Direct Counterfactual Marketing Optimization](https://mlsanity.com/paper/2407.13664/) (2024)
- [Solver-Free Decision-Focused Learning for Linear Optimization Problems](https://mlsanity.com/paper/2505.22224/) (2025)
- [Improving Generative Ad Text on Facebook using Reinforcement Learning](https://mlsanity.com/paper/2507.21983/) (2025)
- [Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regime](https://mlsanity.com/paper/2311.07633/) (2023)
- [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)
- [Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints](https://mlsanity.com/paper/2510.04951/) (2025)
- [Robust Losses for Decision-Focused Learning](https://mlsanity.com/paper/2310.04328/) (2023)
- [Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models](https://mlsanity.com/paper/2409.09684/) (2024)
- [Diffusion-DFL: Decision-focused Diffusion Models for Stochastic Optimization](https://mlsanity.com/paper/2510.11590/) (2025)
- [Scalable Coupling of Deep Learning with Logical Reasoning](https://mlsanity.com/paper/2305.07617/) (2023)
- [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)
- [GenCO: Generating Diverse Designs with Combinatorial Constraints](https://mlsanity.com/paper/2310.02442/) (2023)
- [Continuous Parallel Relaxation for Finding Diverse Solutions in Combinatorial Optimization Problems](https://mlsanity.com/paper/2402.02190/) (2024)
- [Locally Convex Global Loss Network for Decision-Focused Learning](https://mlsanity.com/paper/2403.01875/) (2024)
- [Improve ROI with Causal Learning and Conformal Prediction](https://mlsanity.com/paper/2407.01065/) (2024)
- [Learning Joint Models of Prediction and Optimization](https://mlsanity.com/paper/2409.04898/) (2024)
- [Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach](https://mlsanity.com/paper/2508.10776/) (2025)
- [Decision-Focused Forecasting: A Differentiable Multistage Optimisation Architecture](https://mlsanity.com/paper/2405.14719/) (2024)

## Abstract (arXiv)

In the last years decision-focused learning framework, also known as predict-and-optimize, have received increasing attention. In this setting, the predictions of a machine learning model are used as estimated cost coefficients in the objective function of a discrete combinatorial optimization problem for decision making. Decision-focused learning proposes to train the ML models, often neural network models, by directly optimizing the quality of decisions made by the optimization solvers. Based on a recent work that proposed a noise contrastive estimation loss over a subset of the solution space, we observe that decision-focused learning can more generally be seen as a learning-to-rank problem, where the goal is to learn an objective function that ranks the feasible points correctly. This observation is independent of the optimization method used and of the form of the objective function. We develop pointwise, pairwise and listwise ranking loss functions, which can be differentiated in closed form given a subset of solutions. We empirically investigate the quality of our generic methods compared to existing decision-focused learning approaches with competitive results. Furthermore, controlling the subset of solutions allows controlling the runtime considerably, with limited effect on regret.