Counterfactual Explanations for Integer Optimization Problems

TL;DR

This paper explores counterfactual explanations for integer optimization problems, establishing computational complexity and proposing algorithms for specific cases, with empirical evaluation on knapsack and shortest path problems.

Contribution

It introduces the first complexity analysis for CEs in integer optimization and develops algorithms for key tractable cases, filling a research gap.

Findings

CE construction is $^p$-complete even for simple binary programs

Algorithms effectively generate CEs for mutable parameters in classical problems

Empirical results demonstrate practical applicability on knapsack and shortest path instances

Abstract

Counterfactual explanations (CEs) offer a human-understandable way to explain decisions by identifying specific changes to the input parameters of a base or present model that would lead to a desired change in the outcome. For optimization models, CEs have primarily been studied in limited contexts and little research has been done on CEs for general integer optimization problems. In this work, we address this gap. We first show that the general problem of constructing a CE is $\Sigma_2^p$-complete even for binary integer programs with just a single mutable constraint. Second, we propose solution algorithms for several of the most tractable special cases: (i) mutable objective parameters, (ii) a single mutable constraint, (iii) mutable right-hand-side, and (iv) all input parameters can be modified. We evaluate our approach using classical knapsack problem instances, focusing on cases with mutable constraint parameters. Additionally, we present experiments on the resource constrained shortest path problem.