Abstract
In this work we present a sampling-based algorithm designed to solve game-theoretic control problems and risk-sensitive stochastic optimal control problems. The cornerstone of the proposed approach is the formulation of the problem in terms of forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear version of the Feynman-Kac lemma, we obtain a probabilistic representation of the solution to the nonlinear Hamilton-Jacobi-Isaacs equation, expressed in the form of a decoupled system of FBSDEs. This system of FBSDEs can then be simulated by employing linear regression techniques. Utilizing the connection between stochastic differential games and risk-sensitive optimal control, we demonstrate that the proposed algorithm is also applicable to the latter class of problems. Simulation results validate the algorithm.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call