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In this paper, we present an efficient algorithm for solving a class ofchance constrained optimization under non-parametric uncertainty. Our algorithmis built on the possibility of representing arbitrary distributions asfunctions in Reproducing Kernel Hilbert Space (RKHS). We use this foundation toformulate chance constrained optimization as one of minimizing the distancebetween a desired distribution and the distribution of the constraint functionsin the RKHS. We provide a systematic way of constructing the desireddistribution based on a notion of scenario approximation. Furthermore, we usethe kernel trick to show that the computational complexity of our reformulatedoptimization problem is comparable to solving a deterministic variant of thechance-constrained optimization. We validate our formulation on two importantrobotic/control applications: (i) reactive collision avoidance of mobile robotsin uncertain dynamic environments and (ii) inverse dynamics based path trackingof manipulators under perception uncertainty. In both these applications, theunderlying chance constraints are defined over highly non-linear and non-convexfunctions of the uncertain parameters and possibly also decision variables. Wealso benchmark our formulation with the existing approaches in terms of samplecomplexity and the achieved optimal cost highlighting significant improvementsin both these metrics.

Solving Chance Constrained Optimization under Non-Parametric Uncertainty Through Hilbert Space Embedding