Inverse Optimization via Learning Feasible Regions

TL;DR

This paper introduces a novel inverse optimization method that learns feasible regions for linear objectives, capturing complex behaviors and validated through power system applications and synthetic experiments.

Contribution

It proposes a new hypothesis class for learning feasible regions, along with a specialized algorithm, improving over prior objective-only inverse optimization methods.

Findings

Outperforms existing methods in synthetic tests

Effectively captures discontinuous behaviors in data

Validated on power system applications

Abstract

We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective function, as learning the constraint function (i.e., feasible regions) leads to nonconvex training programs. Motivated by this, we focus on learning feasible regions for known linear objectives and introduce two training losses along with a hypothesis class to parameterize the constraint function. Our hypothesis class surpasses the previous objective-only method by naturally capturing discontinuous behaviors in input-decision pairs. We introduce a customized block coordinate descent algorithm with a smoothing technique to solve the training problems, while for further restricted hypothesis classes, we reformulate the training optimization as a tractable convex program or mixed integer linear program. Synthetic experiments and two power system applications, including comparisons with state-of-the-art approaches, showcase and validate the proposed approach.