Actor-Critic learning for mean-field control in continuous time

• URL: http://arxiv.org/abs/2303.06993v1
• Date: Mon, 13 Mar 2023 10:49:25 GMT
• Title: Actor-Critic learning for mean-field control in continuous time
• Authors: Noufel Frikha (UP1 UFR27), Maximilien Germain (LPSM (UMR\_8001)), Mathieu Lauri\`ere, Huy\^en Pham (LPSM (UMR\_8001)), Xuanye Song (LPSM (UMR\_8001))
• Abstract summary: We study policy gradient for mean-field control in continuous time in a reinforcement learning setting. By considering randomised policies with entropy regularisation, we derive a gradient expectation representation of the value function. In the linear-quadratic mean-field framework, we obtain an exact parametrisation of the actor and critic functions defined on the Wasserstein space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study policy gradient for mean-field control in continuous time in a reinforcement learning setting. By considering randomised policies with entropy regularisation, we derive a gradient expectation representation of the value function, which is amenable to actor-critic type algorithms, where the value functions and the policies are learnt alternately based on observation samples of the state and model-free estimation of the population state distribution, either by offline or online learning. In the linear-quadratic mean-field framework, we obtain an exact parametrisation of the actor and critic functions defined on the Wasserstein space. Finally, we illustrate the results of our algorithms with some numerical experiments on concrete examples.

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