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This paper employs a policy iteration reinforcement learning (RL) method toinvestigate continuous-time mean-field linear quadratic problems over aninfinite horizon. The drift and diffusion terms in the dynamics involve thestate as well as the control. The stability and convergence of the RL algorithmare examined using a Lyapunov Recursion. Instead of solving a pair of coupledRiccati equations, the RL technique focuses on strengthening an auxiliaryfunction and the cost functional as the objective functions and updating thenew policy to compute the optimal control via state trajectories. A numericalexample sheds light on the established theoretical results.

Policy Iteration Reinforcement Learning Method for Continuous-time Mean-Field Linear-Quadratic Optimal Problem