Solving Time-Continuous Stochastic Optimal Control Problems: Algorithm Design and Convergence Analysis of Actor-Critic Flow

We propose an actor-critic framework to solve the time-continuous stochastic optimal control problem. A least square temporal difference method is applied to compute the value function for the critic. The policy gradient method is implemented as policy improvement for the actor. Our key contribution lies in establishing the global convergence property of our proposed actor-critic flow, demonstrating a linear rate of convergence. Theoretical findings are further validated through numerical examples, showing the efficacy of our approach in practical applications.