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arXiv · 2503.20510

Extended mean field control: a global numerical solution via finite-dimensional approximation

Athena Picarelli·Marco Scaratti·Jonathan Tam
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Abstract

We investigate the global numerical approximation of a class of extended mean field control problems (MFC), where the dynamics and costs depend on the joint distribution of the state and the control. We propose a framework to approximate the value function globally over the Wasserstein space, moving beyond the restriction of fixed initial conditions. Our approach exploits the propagation of chaos by approximating the infinite-dimensional MFC problem by an $N$-player cooperative game, together with the usage of finite-dimensional solvers. This method avoids the need to parametrise functions on an infinite-dimensional space, offering a balance between probabilistic rigor and computational efficiency.

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Athena Picarelli, Marco Scaratti, Jonathan Tam. 2025-03-26. Extended mean field control: a global numerical solution via finite-dimensional approximation. https://arxiv.org/abs/2503.20510

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