A Policy Gradient Framework for Stochastic Optimal Control Problems with Global Convergence Guarantee

In this work, we consider the stochastic optimal control problem in continuous time and a policy gradient method to solve it. In particular, we study the gradient flow for the control, viewed as a continuous time limit of the policy gradient. We prove the global convergence of the gradient flow and establish a convergence rate under some regularity assumptions. The main novelty in the analysis is the notion of local optimal control function, which is introduced to compare the local optimality of the iterate.