Neural Approximations of the Solutions to a Class of Stochastic Optimal Control Problems

Abstract

The approximate solution of ï¬nite-horizon optimal control problems via neural approximations of the optimal closed-loop control functions is investigated. The analysis enhances the potentialities of recent developments in neural-network approximation in the framework of sequential decision problems with continuous state and control spaces. A class of stochastic optimal control problems with bilinear dynamical systems is investigated, for which neural-network approximation mitigates the curse of dimensionality. More speciï¬cally, the minimal number of network parameters needed to achieve a desired accuracy of the approximate solution does not grow exponentially with the number of state variables. The results obtained provide a theoretical basis to the development of neural-network-based approaches for the suboptimal control of stochastic dynamical systems.