Deep neural network expressivity for optimal stopping problems

Understand

This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces.

• A general framework is established in which the value function and continuation value of an optimal stopping problem can be approximated with error at most $\varepsilon$ by a deep ReLU neural network of size at most $\kappa d^{\mathfrak{q}} \varepsilon^{-\mathfrak{r}}$.
• The constants $\kappa,\mathfrak{q},\mathfrak{r} \geq 0$ do not depend on the dimension $d$ of the state space or the approximation accuracy $\varepsilon$.
• This proves that deep neural networks do not suffer from the curse of dimensionality when employed to solve optimal stopping problems.