Scalable Kernel Inverse Optimization

TL;DR

This paper introduces a scalable kernel-based inverse optimization framework that leverages RKHS to enhance feature representation, along with an efficient training algorithm, validated on MuJoCo benchmarks.

Contribution

It extends inverse optimization to RKHS, proposes a scalable training algorithm, and demonstrates improved generalization in learning-from-demonstration tasks.

Findings

The KIO model effectively learns objective functions in high-dimensional spaces.

The SSO algorithm improves training efficiency for kernel inverse optimization.

Experimental results show strong generalization on MuJoCo benchmarks.

Abstract

Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert space (RKHS), thereby enhancing feature representation to an infinite-dimensional space. We demonstrate that a variant of the representer theorem holds for a specific training loss, allowing the reformulation of the problem as a finite-dimensional convex optimization program. To address scalability issues commonly associated with kernel methods, we propose the Sequential Selection Optimization (SSO) algorithm to efficiently train the proposed Kernel Inverse Optimization (KIO) model. Finally, we validate the generalization capabilities of the proposed KIO model and the effectiveness of the SSO algorithm through learning-from-demonstration tasks on the MuJoCo benchmark.