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Forward-Backward Rapidly-Exploring Random Trees for Stochastic Optimal Control

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Document pages: 8 pages

Abstract: We propose a numerical method for the computation of the forward-backwardstochastic differential equations (FBSDE) appearing in the Feynman-Kacrepresentation of the value function in stochastic optimal control problems. Bythe use of the Girsanov change of probability measures, it is demonstrated howa rapidly-exploring random tree (RRT) method can be utilized for the forwardintegration pass, as long as the controlled drift terms are appropriatelycompensated in the backward integration pass. Subsequently, a numericalapproximation of the value function is proposed by solving a series of functionapproximation problems backwards in time along the edges of the constructedRRT. Moreover, a local entropy-weighted least squares Monte Carlo (LSMC) methodis developed to concentrate function approximation accuracy in regions mostlikely to be visited by optimally controlled trajectories. The results of theproposed methodology are demonstrated on linear and nonlinear stochasticoptimal control problems with non-quadratic running costs, which revealsignificant convergence improvements over previous FBSDE-based numericalsolution methods.

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