Rates of convergence for the policy iteration method for Mean Field Games systems

TL;DR

This paper analyzes the convergence rate of the policy iteration method applied to Mean Field Games systems, providing estimates that enhance understanding of its efficiency and speed.

Contribution

It offers the first estimate of the convergence rate for the policy iteration method in Mean Field Games, extending previous convergence proofs.

Findings

Convergence of the policy iteration method is established for Mean Field Games.

An estimate of the convergence rate is provided, indicating potential quadratic convergence.

Results improve understanding of algorithm efficiency in Mean Field Games contexts.

Abstract

Convergence of the policy iteration method for discrete and continuous optimal control problems holds under general assumptions. Moreover, in some circumstances, it is also possible to show a quadratic rate of convergence for the algorithm. For Mean Field Games, convergence of the policy iteration method has been recently proved in [9]. Here, we provide an estimate of its rate of convergence.