Relative Explanations for Contextual Problems with Endogenous Uncertainty: An Application to Competitive Facility Location

TL;DR

This paper introduces a novel method for generating interpretable counterfactual explanations in complex stochastic optimization problems with endogenous uncertainty, demonstrated through a competitive facility location case study.

Contribution

It is the first to focus on relative explanations for problems with binary decisions and endogenous uncertainty, using Wasserstein regularization for efficiency.

Findings

Efficient computation of sparse, interpretable explanations achieved.

Wasserstein regularization reduces computation times.

Method successfully applied to a facility location problem.

Abstract

In this paper, we consider contextual stochastic optimization problems under endogenous uncertainty, where decisions affect the underlying distributions. To implement such decisions in practice, it is crucial to ensure that their outcomes are interpretable and trustworthy. To this end, we compute relative counterfactual explanations that provide practitioners with concrete changes in the contextual covariates required for a solution to satisfy specific constraints. Whereas relative explanations have been introduced in prior literature, to the best of our knowledge this is the first work focusing on problems with binary decision variables and endogenous uncertainty. We propose a methodology that uses the Wasserstein distance as a regularization term, which leads to a reduction in computation times compared to its unregularized counterpart. We illustrate the method using a choice-based competitive facility location problem and present numerical experiments that demonstrate its ability to efficiently compute sparse and interpretable explanations.