Learning Optimal Policies in Potential Mean Field Games: Smoothed Policy Iteration Algorithms

.We introduce two smoothed policy iteration algorithms (SPIs) as rules for learning policies and methods for computing Nash equilibria in second order potential mean field games (MFGs). Global convergence is proved if the coupling term in the MFG system satisfies the Lasry–Lions monotonicity condition. Local convergence to a stable solution is proved for a system which may have multiple solutions. The convergence analysis shows close connections between SPIs and the fictitious play algorithm, which has been widely studied in the MFG literature. Numerical simulation results based on finite difference schemes are presented to supplement the theoretical analysis.Keywordsmean field gamespolicy iterationlearning in gamesnumerical methodsMSC codes49N7091A1335Q8065M06