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

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 ML model to optimize the quality of the decisions made using the predicted parameters. When parameters in the constraints of a COP are predicted, the predicted parameters 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 linear program (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 when the predicted parameters lead to infeasible solutions), and the second one penalizes suboptimal decisions (by penalizing when the true optimal solution is infeasible under the predicted parameters). 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 a decision-maker the control over the trade-off between the two. Moreover, across several COP instances, we find that for a single value of the tunable parameter, our method matches the performance of the existing baselines on suboptimality and feasibility.