Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence Analysis of Machine Learning Algorithms for the Numerical
  Solution of Mean Field Control and Games: II -- The Finite Horizon Case   We propose two numerical methods for the optimal control of McKean-Vlasov
dynamics in finite time horizon. Both methods are based on the introduction of
a suitable loss function defined over the parameters of a neural network. This
allows the use of machine learning tools, and efficient implementations of
stochastic gradient descent in order to perform the optimization. In the first
method, the loss function stems directly from the optimal control problem. The
second method tackles a generic forward-backward stochastic differential
equation system (FBSDE) of McKean-Vlasov type, and relies on suitable
reformulation as a mean field control problem. To provide a guarantee on how
our numerical schemes approximate the solution of the original mean field
control problem, we introduce a new optimization problem, directly amenable to
numerical computation, and for which we rigorously provide an error rate.
Several numerical examples are provided. Both methods can easily be applied to
certain problems with common noise, which is not the case with the existing
technology. Furthermore, although the first approach is designed for mean field
control problems, the second is more general and can also be applied to the
FBSDE arising in the theory of mean field games.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat