Finite-horizon mean field control and game problems can be approximated by training neural networks, with explicit error rates in population size, network width, and time step.
Deep Learning Methods for Mean Field Control Problems with Delay
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abstract
We consider a general class of mean field control problems described by stochastic delayed differential equations of McKean-Vlasov type. Two numerical algorithms are provided based on deep learning techniques, one is to directly parameterize the optimal control using neural networks, the other is based on numerically solving the McKean-Vlasov forward anticipated backward stochastic differential equation (MV-FABSDE) system. In addition, we establish a necessary and sufficient stochastic maximum principle for this class of mean field control problems with delay based on the differential calculus on function of measures, as well as existence and uniqueness results for the associated MV-FABSDE system.
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2019 1verdicts
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Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Case
Finite-horizon mean field control and game problems can be approximated by training neural networks, with explicit error rates in population size, network width, and time step.