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arXiv · 2004.00166

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

Jia-Jie Zhu·Wittawat Jitkrittum·Moritz Diehl·Bernhard Schölkopf
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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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Jia-Jie Zhu, Wittawat Jitkrittum, Moritz Diehl, Bernhard Schölkopf. 2020-03-31. Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem. https://arxiv.org/abs/2004.00166

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