Work

Policy Iteration Reinforcement Learning Method for Continuous-Time Linear–Quadratic Mean-Field Control Problems

Year: 2024

Type: article

Abstract: In this article, we employ a policy iteration reinforcement learning (RL) method to study continuous-time linear–quadratic mean-field control problems in infinite horizon. The drift and diffusion terms in the dynamics involve the states, the controls, and their conditional expectations. We investigate the stabilizability and convergence of the RL algorithm using a Lyapunov recursion. Instead of solving a pair of coupled Riccati equations, the RL technique focuses on strengthening an auxiliary function and the cost functional as the objective functions and updating the new policy to compute the optimal control via state trajectories. A numerical example sheds light on the established theoretical results.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2024.3494656

Authors: Na Li, Xun Li, Zuo Quan Xu

Institutions: Shandong University of Finance and Economics, Hong Kong Polytechnic University

Language: English

Topic: Adaptive Dynamic Programming Control

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Hong Kong Polytechnic University

Awards: G213983658, G7553310024