Objective-Based Counterfactual Explanations for Linear Discrete Optimization

Anton Korikov, J. Christopher Beck

Abstract: Given a user who asks why an algorithmic decision did not satisfy some conditions, a counterfactual explanation takes the form of a minimally perturbed input that would have led to a decision satisfying the user’s conditions. Building on recent work, this paper develops techniques to generate counterfactual explanations for linear discrete constrained optimization problems. These explanations take the form of a minimally perturbed objective vector that induces an optimal solution satisfying the newly stated user constraints. Drawing inspiration from the inverse combinatorial optimization literature, we introduce a novel non-convex quadratic programming algorithm to generate such explanations. Furthermore, we develop conditions for the existence of an explanation, addressing a limitation of past approaches. Finally, we discuss several future directions for explanations in discrete optimization such as actionable and sparse explanations.