Scalable Kernel Inverse Optimization
This work addresses scalability in kernel-based inverse optimization for learning-from-demonstration tasks, representing an incremental improvement.
The paper tackles the problem of learning objective functions in inverse optimization by extending them to a reproducing kernel Hilbert space, and demonstrates improved generalization on MuJoCo benchmark tasks through a scalable algorithm.
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.