  Recent work on Path-Dependent Partial Differential Equations (PPDEs) has
shown that PPDE solutions can be approximated by a probabilistic
representation, implemented in the literature by the estimation of conditional
expectations using regression. However, a limitation of this approach is to
require the selection of a basis in a function space. In this paper, we
overcome this limitation by the use of deep learning methods, and we show that
this setting allows for the derivation of error bounds on the approximation of
conditional expectations. Numerical examples based on a two-person zero-sum
game, as well as on Asian and barrier option pricing, are presented. In
comparison with other deep learning approaches, our algorithm appears to be
more accurate, especially in large dimensions.
