Preprints, Working Papers, ... Year : 2024

Optimal control under unknown intensity with Bayesian learning

Abstract

We consider an optimal control problem inspired by neuroscience, where the dynamics is driven by a Poisson process with a controlled stochastic intensity and an uncertain parameter. Given a prior distribution for the unknown parameter, we describe its evolution according to Bayes' rule. We reformulate the optimization problem using 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.

Dates and versions

hal-04826347 , version 1 (09-12-2024)

Licence

Identifiers

Cite

Nicolas Baradel, Quentin Cormier. Optimal control under unknown intensity with Bayesian learning. 2024. ⟨hal-04826347⟩
13 View
0 Download

Altmetric

Share

More