The Pontryagin maximum principle and $Q$-functions in rough environments
Optimization and Control
2026-01-12 v1 Probability
Abstract
We derive the Pontryagin maximum principle and -functions for the relaxed control of noisy rough differential equations. Our main tool is the development of a novel differentiation procedure along `spike variation' perturbations of the optimal state-control pair. We then exploit our development of the infinitesimal -function (also known as the -function) to derive a policy improvement algorithm for settings with entropic cost constraints.
Keywords
Cite
@article{arxiv.2601.05354,
title = {The Pontryagin maximum principle and $Q$-functions in rough environments},
author = {Estepan Ashkarian and Prakash Chakraborty and Harsha Honnappa and Samy Tindel},
journal= {arXiv preprint arXiv:2601.05354},
year = {2026}
}