Recurrent neural networks for stochastic control problems with delay

Stochastic control problems with delay are challenging due to the path-dependent feature of system and thus its intrinsic high dimensions. In this paper, we propose systematically study deep neural network-based algorithms solve stochastic features. Specifically, employ networks for sequence modeling (e.g., recurrent such as long short-term memory) parameterize policy optimize objective function. The proposed tested on three benchmark examples: a linear-quadratic problem, optimal consumption fixed finite delay, portfolio optimization complete memory. Particularly, notice that architecture naturally captures much flexibility yields better performance more efficient stable training network compared feedforward networks. superiority is even evident in case memory, which features infinite delay.