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Learning algorithms for mean field optimal control

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arxiv 2503.17869 v1 pith:AQ4OOMJ5 submitted 2025-03-22 math.OC

H. Mete Soner , Josef Teichmann , Qinxin Yan This is my paper · ORCID
classification math.OC
keywords optimalcontroladditionalgorithmalgorithmsanalysisanalyzeapproximate
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abstract

We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle system and leverage the exchangeability of the particles to obtain substantial computational efficiency. In addition to several numerical examples, a convergence analysis is provided. We also developed a universal approximation theorem on Wasserstein spaces.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Iterative Schemes for Markov Perfect Equilibria

    math.OC 2025-07 conditional novelty 7.0 of 10

    Picard and weighted Picard best-response iterations converge geometrically to the unique Markov perfect equilibrium in symmetric finite-state continuous-time games, with no Lasry-Lions monotonicity needed.

  2. Actor-Critic Learning for Extended Mean Field Control with Deterministic Policies

    math.OC 2026-07 accept novelty 6.0 of 10

    Model-free deterministic policy gradients and a continuous-time deep actor-critic algorithm solve extended mean-field control problems whose dynamics and rewards depend on the joint state-control law.

  3. Neural feedback approximation for stochastic control with degenerate diffusions: error estimates and numerical analysis

    math.OC 2026-07 conditional novelty 6.0 of 10

    Direct neural feedback learning for time-discrete stochastic control admits an averaged value-error bound without transition-density assumptions, covering degenerate and deterministic dynamics.

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