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arXiv · 2009.08175

Optimal regularity of extended mean field controls and their piecewise constant approximation

Christoph Reisinger·Wolfgang Stockinger·Yufei Zhang
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Abstract

We consider the control of McKean-Vlasov dynamics whose coefficients have mean field interactions in the state and control. We show that for a class of linear-convex mean field control problems, the unique optimal open-loop control admits the optimal 1/2-H\"{o}lder regularity in time. Consequently, we prove that the value function can be approximated by one with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping, up to an order 1/2 error, and the optimal control can be approximated up to an order 1/4 error. These results are novel even for the case without mean field interaction.

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Christoph Reisinger, Wolfgang Stockinger, Yufei Zhang. 2020-09-17. Optimal regularity of extended mean field controls and their piecewise constant approximation. https://arxiv.org/abs/2009.08175

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