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Deep Policy Iteration for high-dimensional mean field games

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  • Assouli, Mouhcine
  • Missaoui, Badr

Abstract

This paper introduces Deep Policy Iteration (DPI), a novel approach that integrates the strengths of Neural Networks with the stability and convergence advantages of Policy Iteration (PI) to address high-dimensional stochastic Mean Field Games (MFG). DPI overcomes the limitations of PI, which is constrained by the curse of dimensionality to low-dimensional problems, by iteratively training three neural networks to solve PI equations and satisfy forward-backwards conditions. Our findings indicate that DPI achieves comparable convergence levels to the Mean Field Deep Galerkin Method (MFDGM), with additional advantages. Furthermore, deep learning techniques show promise in handling separable Hamiltonian cases where PI alone is less effective. DPI effectively manages high-dimensional problems, extending the applicability of PI to both separable and non-separable Hamiltonians.

Suggested Citation

  • Assouli, Mouhcine & Missaoui, Badr, 2024. "Deep Policy Iteration for high-dimensional mean field games," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    • Handle: RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324003849
    DOI: 10.1016/j.amc.2024.128923
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    References listed on IDEAS

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    1. Assouli, Mouhcine & Missaoui, Badr, 2023. "Deep learning for Mean Field Games with non-separable Hamiltonians," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Valerio Capraro & Roberto Di Paolo & Matjaz Perc & Veronica Pizziol, 2024. "Language-based game theory in the age of artificial intelligence," Papers 2403.08944, arXiv.org.
    3. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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