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We present SOCKS, a data-driven stochastic optimal control toolbox based inkernel methods. SOCKS is a collection of data-driven algorithms that computeapproximate solutions to stochastic optimal control problems with arbitrarycost and constraint functions, including stochastic reachability, which seeksto determine the likelihood that a system will reach a desired target set whilerespecting a set of pre-defined safety constraints. Our approach relies upon aclass of machine learning algorithms based in kernel methods, a nonparametrictechnique which can be used to represent probability distributions in ahigh-dimensional space of functions known as a reproducing kernel Hilbertspace. As a nonparametric technique, kernel methods are inherently data-driven,meaning that they do not place prior assumptions on the system dynamics or thestructure of the uncertainty. This makes the toolbox amenable to a wide varietyof systems, including those with nonlinear dynamics, black-box elements, andpoorly characterized stochastic disturbances. We present the main features ofSOCKS and demonstrate its capabilities on several benchmarks.

SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods