Scalable Kernel Inverse Optimization

• URL: http://arxiv.org/abs/2410.23952v1
• Date: Thu, 31 Oct 2024 14:06:43 GMT
• Title: Scalable Kernel Inverse Optimization
• Authors: Youyuan Long, Tolga Ok, Pedro Zattoni Scroccaro, Peyman Mohajerin Esfahani,
• Abstract summary: Inverse optimization is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. We extend the hypothesis class of IO objective functions to a reproducing a kernel Hilbert space. We show 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.
• Score: 2.799896314754615
• License:
• 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.

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