# Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints

arXiv: https://arxiv.org/abs/2510.04951 · HTML: https://mlsanity.com/paper/2510.04951/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 34 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## 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)
- [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)
- [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)
- [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)
- [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)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Learning with Combinatorial Optimization Layers: a Probabilistic Approach](https://mlsanity.com/paper/2207.13513/) (2022)
- [Alternating Differentiation for Optimization Layers](https://mlsanity.com/paper/2210.01802/) (2022)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [Predict+Optimize for Packing and Covering LPs with Unknown Parameters in Constraints](https://mlsanity.com/paper/2209.03668/) (2022)
- [Solver-Free Decision-Focused Learning for Linear Optimization Problems](https://mlsanity.com/paper/2505.22224/) (2025)
- [Learning MAX-SAT from Contextual Examples for Combinatorial Optimisation](https://mlsanity.com/paper/2202.03888/) (2022)
- [CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs](https://mlsanity.com/paper/2312.07718/) (2023)
- [A Solver-Free Framework for Scalable Learning in Neural ILP Architectures](https://mlsanity.com/paper/2210.09082/) (2022)
- [Branch & Learn with Post-hoc Correction for Predict+Optimize with Unknown Parameters in Constraints](https://mlsanity.com/paper/2303.06698/) (2023)
- [Scalable Coupling of Deep Learning with Logical Reasoning](https://mlsanity.com/paper/2305.07617/) (2023)
- [Learning to Learn in Interactive Constraint Acquisition](https://mlsanity.com/paper/2312.10795/) (2023)
- [Decision-Focused Learning to Predict Action Costs for Planning](https://mlsanity.com/paper/2408.06876/) (2024)

## Built on by (most cited first, 6 of 6)

- [DePICT: Decision-Preserving Interface for Constrained Downstream Tasks](https://mlsanity.com/paper/2610.03945/) (2026)
- [Imitation Learning for Combinatorial Optimisation under Uncertainty](https://mlsanity.com/paper/2601.05383/) (2026)
- [Decision-Focused Learning in Network Interdiction Games](https://mlsanity.com/paper/2608.09036/) (2026)
- [Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift](https://mlsanity.com/paper/2608.29465/) (2026)
- [PolyStepOR: Learning to Decide Without Optimal Decisions](https://mlsanity.com/paper/2609.32465/) (2026)
- [RL-PaO: Prediction as Action in Decision Making under Uncertainty](https://mlsanity.com/paper/2609.37065/) (2026)

## Abstract (arXiv)

When some parameters of a constrained optimization problem (COP) are uncertain, this gives rise to a predict-then-optimize (PtO) problem, comprising two stages: the prediction of the unknown parameters from contextual information and the subsequent optimization using those predicted parameters. Decision-focused learning (DFL) implements the first stage by training a machine learning (ML) model to optimize the quality of the decisions made using the predicted parameters. When the predicted parameters occur in the constraints, they can lead to infeasible solutions. Therefore, it is important to simultaneously manage both feasibility and decision quality. We develop a DFL framework for predicting constraint parameters in a generic COP. While prior works typically assume that the underlying optimization problem is a linear program (LP) or integer LP (ILP), our approach makes no such assumption. We derive two novel loss functions based on maximum likelihood estimation (MLE): the first one penalizes infeasibility (by penalizing predicted parameters that lead to infeasible solutions), while the second one penalizes suboptimal decisions (by penalizing predicted parameters that make the true optimal solution infeasible). We introduce a single tunable parameter to form a weighted average of the two losses, allowing decision-makers to balance suboptimality and feasibility. We experimentally demonstrate that adjusting this parameter provides decision-makers control over this trade-off. Moreover, across several COP instances, we show that adjusting the tunable parameter allows a decision-maker to prioritize either suboptimality or feasibility, outperforming the performance of existing baselines in either objective.