Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem

• URL: http://arxiv.org/abs/2004.00166v2
• Date: Sun, 6 Sep 2020 15:02:55 GMT
• Title: Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem
• Authors: Jia-Jie Zhu, Wittawat Jitkrittum, Moritz Diehl, Bernhard Sch\"olkopf
• Abstract summary: We propose to quantify the worst-case risk under distributional ambiguity using the kernel mean embedding. We numerically test the proposed method in characterizing the worst-case constraint violation probability in the context of a constrained control system.
• Score: 17.909696462645023
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kernel mean embedding. Specifically, we formulate the generalized moment problem whose ambiguity set (i.e., the moment constraint) is described by constraints in the associated reproducing kernel Hilbert space in a nonparametric manner. We then present the tractable approximation and its theoretical justification. As a concrete application, we numerically test the proposed method in characterizing the worst-case constraint violation probability in the context of a constrained stochastic control system.

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