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Near Optimal Finite Model POMDP Approximation of Controlled Diffusion with Partial Information

Yunus Emre Demirci, Somnath Pradhan, Serdar Yüksel · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28377 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

Nuestras principales contribuciones son las siguientes: (i) Mostramos la cercanía a la optimidad, bajo el horizonte finito, así como los criterios de coste de horizonte infinito descuentados, de las políticas de control constante fragmentadas obtenidas a través de soluciones a las aproximaciones del proceso de decisión de Markov (POMDP) parcialmente observables en tiempo discreto, construidas a través de las aproximaciones de Euler-Maruyama de ambos procesos de estado y observación; (ii) obtenemos varias propiedades de regularidad de tales modelos aproximados de POMDP; y (iii) utilizando estas propiedades de regularidad, llegamos a aproximaciones del modelo finito óptimo. (iv) Estos culminan en nuestro resultado principal, que es que una solución óptima para el modelo finito aproximado de POMDP está cerca de la óptima

Machine translation (Meta M2M100); the English original follows.

Abstract

We study continuous-time stochastic control problems under partial information. Our main contributions are the following: (i) We show near optimality, under finite horizon as well as discounted infinite horizon cost criteria, of piece-wise constant control policies obtained via solutions to discrete-time partially observable Markov decision process (POMDP) approximations, constructed via Euler-Maruyama approximations of both state and observation processes; (ii) we obtain several regularity properties of such POMDP approximate models; and (iii) using these regularity properties, we arrive at near optimal finite model approximations. (iv) These culminate into our main result which is that an optimal solution for the approximate finite POMDP model is near optimal for the original diffusion with partial information.

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Topics: Partially observable Markov decision process, Optimal control, Mathematics, Observable, Markov process, Applied mathematics

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