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In order to anticipate rare and impactful events, we propose to quantify theworst-case risk under distributional ambiguity using a recent development inkernel methods -- the kernel mean embedding. Specifically, we formulate thegeneralized moment problem whose ambiguity set (i.e., the moment constraint) isdescribed by constraints in the associated reproducing kernel Hilbert space ina nonparametric manner. We then present the tractable approximation and itstheoretical justification. As a concrete application, we numerically test theproposed method in characterizing the worst-case constraint violationprobability in the context of a constrained stochastic control system.

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