Learning Stochastic Optimal Policies via Gradient Descent
Abstract
We systematically develop a learning-based treatment of stochastic optimal control (SOC), relying on direct optimization of parametric control policies. We propose a derivation of adjoint sensitivity results for stochastic differential equations through direct application of variational calculus. Then, given an objective function for a predetermined task specifying the desiderata for the controller, we optimize their parameters via iterative gradient descent methods. In doing so, we extend the range of applicability of classical SOC techniques, often requiring strict assumptions on the functional form of system and control. We verify the performance of the proposed approach on a continuous-time, finite horizon portfolio optimization with proportional transaction costs.
Cite
@article{arxiv.2106.03780,
title = {Learning Stochastic Optimal Policies via Gradient Descent},
author = {Stefano Massaroli and Michael Poli and Stefano Peluchetti and Jinkyoo Park and Atsushi Yamashita and Hajime Asama},
journal= {arXiv preprint arXiv:2106.03780},
year = {2021}
}