Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints
Jayanta Mandi, Marianne Defresne, Senne Berden, Tias Guns
TL;DR
This work tackles predict-then-optimize when constraint parameters are uncertain by introducing Odece, a decision-focused learning framework that predicts constraint parameters and trains with two maximum-likelihood–based losses: IPL, which penalizes infeasibility induced by predictions, and OPL, which preserves the true optimum by maintaining feasibility of the known optimal solution. A single tunable parameter $α$ blends these losses to allow decision-makers to trade off suboptimality and infeasibility according to preference. The approach is general beyond LP/ILP, demonstrated on multi-dimensional knapsack and brass alloy production problems, and shows that appropriate tuning of $α$ yields favorable trade-offs against strong baselines, with improved feasibility and competitive regret. This enables practical, end-to-end control over the feasibility-quality balance in constrained optimization under uncertainty, with potential applicability to a wide range of COPs and real-world decision-making settings.
Abstract
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.