Scalable Kernel Inverse Optimization

Youyuan Long, Tolga Ok, Pedro Zattoni Scroccaro, Peyman Mohajerin Esfahani

Keywords: Optimization, Imitation Learning, Inverse Optimization

TL;DR: Proposing a kernel-based Inverse Optimization model with a scalable algorithm designed for imitation learning tasks.

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.

Primary Area: Optimization (convex and non-convex, discrete, stochastic, robust)

Submission Number: 19485