Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Convergence Analysis

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate programming approaches, we first the optimal policy by means of neural networks in spirit reinforcement learning, then value function Monte Carlo regression. is achieved recursion performance or hybrid iteration, regress now methods from numerical probabilities. We provide a theoretical justification these algorithms. Consistency rate convergence estimates are analyzed expressed terms universal approximation error networks, statistical when estimating network function, leaving aside optimization error. Numerical results various applications presented companion (arxiv.org/abs/1812.05916) illustrate proposed