2020/06/22 by Kelsey P. Hawkins, Hawkins, Kelsey P., Ali Pakniyat +5
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Forecasting Techniques and Applications #Gaussian Processes and Bayesian Inference #Optimization and Control (math.OC) #Robotics (cs.RO) #Stochastic processes and financial applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2006.12444
openalex publication_date 2020/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a numerical method for the computation of the forward-backward\nstochastic differential equations (FBSDE) appearing in the Feynman-Kac\nrepresentation of the value function in stochastic optimal control problems. By\nthe use of the Girsanov change of probability measures, it is demonstrated how\na rapidly-exploring random tree (RRT) method can be utilized for the forward\nintegration pass, as long as the controlled drift terms are appropriately\ncompensated in the backward integration pass. Subsequently, a numerical\napproximation of the value function is proposed by solving a series of function\napproximation problems backwards in time along the edges of the constructed\nRRT. Moreover, a local entropy-weighted least squares Monte Carlo (LSMC) method\nis developed to concentrate function approximation accuracy in regions most\nlikely to be visited by optimally controlled trajectories. The results of the\nproposed methodology are demonstrated on linear and nonlinear stochastic\noptimal control problems with non-quadratic running costs, which reveal\nsignificant convergence improvements over previous FBSDE-based numerical\nsolution methods.\n