Solving Chance-Constrained Optimization Under Nonparametric Uncertainty Through Hilbert Space Embedding

In this article, we present an efficient algorithm for solving a class of chance-constrained optimization under nonparametric uncertainty. Our is built on the possibility representing arbitrary distributions as functions in Reproducing Kernel Hilbert Space (RKHS). We use foundation to formulate one minimizing distance between desired distribution and constraint RKHS. provide systematic way constructing based notion scenario approximation. Furthermore, kernel trick show that computational complexity our reformulated problem comparable deterministic variant optimization. validate formulation two important robotic applications: 1) reactive collision avoidance mobile robots uncertain dynamic environments 2) inverse-dynamics-based path-tracking manipulators perception both these applications, underlying chance constraints are defined over nonlinear nonconvex parameters possibly also decision variables. benchmark with existing approaches terms sample achieved optimal cost highlighting significant improvements metrics.