This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming (DP). Diffrently from the classical approximate DP approach, we rst approximate the optimal policy by means of neural networks in the spirit of deep reinforcement learning, and then the value function by Monte Carlo regression. This is achieved in the DP recursion by performance or hybrid iteration, and regress now or later/quantization methods from numerical probabilities. Read more [...]