Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization

TL;DR

This paper introduces a new inverse linear optimization method with an exact algorithm and an adaptive sampling strategy, improving efficiency in data-driven cost estimation and online learning scenarios.

Contribution

It proposes a novel formulation allowing less restrictive cost recovery, an exact solution algorithm, and an adaptive sampling approach for online data updates.

Findings

Efficient algorithms for large-scale inverse optimization problems.

Significant reduction in computational and sampling efforts.

Successful application to customer preference and production planning.

Abstract

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal solutions that correspond to different instances of the linear program. We introduce a new formulation of the problem that, compared to other existing methods, allows the recovery of a less restrictive and generally more appropriate admissible set of cost estimates. It can be shown that this inverse optimization problem yields a finite number of solutions, and we develop an exact two-phase algorithm to determine all such solutions. Moreover, we propose an efficient decomposition algorithm to solve large instances of the problem. The algorithm extends naturally to an online learning environment where it can be used to provide quick updates of the cost estimate as new data becomes available over time. For the online setting, we further develop an effective adaptive sampling strategy that guides the selection of the next samples. The efficacy of the proposed methods is demonstrated in computational experiments involving two applications, customer preference learning and cost estimation for production planning. The results show significant reductions in computation and sampling efforts.