Optimal control under unknown intensity with Bayesian learning - Inria - Institut national de recherche en sciences et technologies du numérique
Pré-Publication, Document De Travail Année : 2024

Optimal control under unknown intensity with Bayesian learning

Résumé

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 et versions

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

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