This paper addresses the fundamental challenge of the 'curse of dimensionality' in stochastic control problems, which makes traditional solution methods computationally infeasible for high-dimensional real-world applications. The authors develop a novel deep learning approach that directly solves these problems by approximating time-dependent controls as feedforward neural networks. These networks are stacked together through the model dynamics, with the control problem's objective function serving as the loss function for the neural network training. The method leverages Monte-Carlo sampling to handle the high-dimensional nature of the problems.

The approach is tested on practical examples from optimal trading and energy storage domains, demonstrating both satisfactory accuracy and the ability to handle high-dimensional scenarios. This represents a significant advancement in stochastic control methodology, providing a computationally feasible framework for real-world applications that were previously intractable due to dimensionality constraints. The integration of deep learning techniques with traditional control theory opens new possibilities for solving complex decision-making problems in finance, energy, and other domains where stochastic control is essential.