Counterfactual Explanations for Linear Optimization

TL;DR

This paper introduces three types of counterfactual explanations for linear optimization, demonstrating that while strong and weak CEs are computationally hard, relative CEs can be efficiently computed by leveraging convex structures, supported by numerical experiments.

Contribution

The paper proposes a novel framework for counterfactual explanations in linear optimization, especially highlighting an efficient method for relative CEs through convex structure exploitation.

Findings

Relative CEs can be computed efficiently, similar to solving the original problem.

Strong and weak CEs are computationally intractable.

Numerical experiments confirm the efficiency of the proposed method.

Abstract

The concept of counterfactual explanations (CE) has emerged as one of the important concepts to understand the inner workings of complex AI systems. In this paper, we translate the idea of CEs to linear optimization and propose, motivate, and analyze three different types of CEs: strong, weak, and relative. While deriving strong and weak CEs appears to be computationally intractable, we show that calculating relative CEs can be done efficiently. By detecting and exploiting the hidden convex structure of the optimization problem that arises in the latter case, we show that obtaining relative CEs can be done in the same magnitude of time as solving the original linear optimization problem. This is confirmed by an extensive numerical experiment study on the NETLIB library.