  This paper presents new machine learning approaches to approximate the
solution of optimal stopping problems. The key idea of these methods is to use
neural networks, where the hidden layers are generated randomly and only the
last layer is trained, in order to approximate the continuation value. Our
approaches are applicable for high dimensional problems where the existing
approaches become increasingly impractical. In addition, since our approaches
can be optimized using a simple linear regression, they are very easy to
implement and theoretical guarantees can be provided. In Markovian examples our
randomized reinforcement learning approach and in non-Markovian examples our
randomized recurrent neural network approach outperform the state-of-the-art
and other relevant machine learning approaches.
