Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints
This work addresses a critical issue in predict-then-optimize settings for decision-makers dealing with uncertain constraint parameters, offering a flexible method to manage feasibility and optimality, though it is incremental as it builds on prior decision-focused learning approaches.
The paper tackles the problem of predicting uncertain parameters in constrained optimization problems where parameters appear in constraints, which can cause infeasible solutions, by developing a decision-focused learning framework with novel loss functions to balance feasibility and decision quality. The result shows that adjusting a tunable parameter allows control over this trade-off, outperforming existing baselines in either objective across several instances.
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.