Deep Learning Approximation for Stochastic Control Problems
This addresses computational challenges in stochastic control for applications like finance and energy, though it appears incremental as it applies existing deep learning techniques to a known bottleneck.
The authors tackled high-dimensional stochastic control problems, which suffer from the curse of dimensionality, by developing a deep learning approach that approximates controls as neural networks and uses the control objective as a loss function, achieving satisfactory accuracy in examples like optimal trading and energy storage.
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo sampling. We approximate the time-dependent controls as feedforward neural networks and stack these networks together through model dynamics. The objective function for the control problem plays the role of the loss function for the deep neural network. We test this approach using examples from the areas of optimal trading and energy storage. Our results suggest that the algorithm presented here achieves satisfactory accuracy and at the same time, can handle rather high dimensional problems.