Near Optimal Finite Model POMDP Approximation of Controlled Diffusion with Partial Information
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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BibTeX
@misc{demirci2026near,
title = {{Near Optimal Finite Model POMDP Approximation of Controlled Diffusion with Partial Information}},
author = {Yunus Emre Demirci and Somnath Pradhan and Serdar Yüksel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28377},
eprint = {2610.28377},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28377},
}
RIS
TY - UNPB
TI - Near Optimal Finite Model POMDP Approximation of Controlled Diffusion with Partial Information
AU - Yunus Emre Demirci
AU - Somnath Pradhan
AU - Serdar Yüksel
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28377
UR - https://arxiv.org/abs/2610.28377
AB - 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.
ER -