Finite-Time Convergence and Regret Guarantees for Neural Reinforcement Learning in POMDPs

Computer Science > Machine Learning

[Submitted on 4 Nov 2026]

Title:Finite-Time Convergence and Regret Guarantees for Neural Reinforcement Learning in POMDPs

View PDF HTML (experimental)Abstract:Reinforcement learning (RL) in Partially Observable Markov Decision Processes (POMDPs) is computationally challenging due to the curse of long-range dependence on history. Fortunately, recent studies have shown that a range of POMDPs that satisfy the filter stability assumption can be well approximated by a superstate Markov Decision Process (MDP) based on a truncated history in a finite-memory window, with a value gap that decays with the window length. However, existing finite-time convergence analyses on such superstate MDP surrogates are either limited to over-simplified linear function approximation or rely on an i.i.d. sampling oracle that is violated by POMDP trajectories, both of which severely limit the applicability of these theoretical results in practice. This motivates us to bridge the gap by investigating RL in POMDPs with nonlinear neural value function approximation. Our main contributions are threefold: i) We first establish a new finite-state MDP point-wise approximation error bound, which lays the foundation for our RL algorithm design and analysis in POMDPs; ii) By applying Temporal-Difference (TD) learning to POMDP-generated superstate transitions and targeting the Bellman fixed point of the superstate MDP, we prove a finite-time critic error bound with nonlinear neural value function approximation; and iii) By combining the neural critic function approximation error bound with the policy mirror descent framework, we obtain a finite-time sublinear regret against the optimal POMDP value. To the best of our knowledge, such a finite-time sublinear regret based on neural function approximation is the first in the literature for finite-memory POMDPs. Our numerical experiments also verify our theoretical results.

Additional Features

References & Citations

Loading...

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)

Connected Papers (What is Connected Papers?)

Litmaps (What is Litmaps?)

scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)

CatalyzeX Code Finder for Papers (What is CatalyzeX?)

DagsHub (What is DagsHub?)

Gotit.pub (What is GotitPub?)

Hugging Face (What is Huggingface?)

ScienceCast (What is ScienceCast?)

Demos

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)

CORE Recommender (What is CORE?)

IArxiv Recommender

(What is IArxiv?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.