Optimal control under unknown intensity with Bayesian learning
Optimization and Control
2025-12-23 v3 Probability
Abstract
We investigate an optimal control problem motivated by neuroscience, where the dynamics is driven by a Poisson process with a controlled stochastic intensity and an unknown parameter. Given a prior distribution for the unknown parameter, we describe its evolution using Bayes' rule. We reformulate the optimization problem by applying Girsanov's theorem and establish a dynamic programming principle. Finally, we characterize the value function as the unique viscosity solution to a finite-dimensional Hamilton-Jacobi-Bellman equation, which can be solved numerically.
Cite
@article{arxiv.2411.04917,
title = {Optimal control under unknown intensity with Bayesian learning},
author = {Nicolas Baradel and Quentin Cormier},
journal= {arXiv preprint arXiv:2411.04917},
year = {2025}
}