Actor critic learning algorithms for mean-field control with moment neural networks

• URL: http://arxiv.org/abs/2309.04317v1
• Date: Fri, 8 Sep 2023 13:29:57 GMT
• Title: Actor critic learning algorithms for mean-field control with moment neural networks
• Authors: Huy\^en Pham and Xavier Warin
• Abstract summary: We develop a new policy gradient and actor-critic algorithm for solving mean-field control problems. The learning for both the actor (policy) and critic (value function) is facilitated by a class of moment neural network functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a new policy gradient and actor-critic algorithm for solving mean-field control problems within a continuous time reinforcement learning setting. Our approach leverages a gradient-based representation of the value function, employing parametrized randomized policies. The learning for both the actor (policy) and critic (value function) is facilitated by a class of moment neural network functions on the Wasserstein space of probability measures, and the key feature is to sample directly trajectories of distributions. A central challenge addressed in this study pertains to the computational treatment of an operator specific to the mean-field framework. To illustrate the effectiveness of our methods, we provide a comprehensive set of numerical results. These encompass diverse examples, including multi-dimensional settings and nonlinear quadratic mean-field control problems with controlled volatility.

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