Learning Stochastic Optimal Policies via Gradient Descent

We systematically develop a learning-based treatment of stochastic optimal control (SOC), relying on direct optimization parametric policies. propose derivation adjoint sensitivity results for differential equations through application variational calculus. Then, given an objective function predetermined task specifying the desiderata controller, we optimize their parameters via iterative gradient descent methods. In doing so, extend range applicability classical SOC techniques, often requiring strict assumptions functional form system and control. verify performance proposed approach continuous-time, finite horizon portfolio with proportional transaction costs.