On Bellman equations for continuous-time policy evaluation I: discretization and approximation

We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with discrete-time reinforcement learning (RL) with function app...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Mou, Wenlong, Zhu, Yuhua
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Online Access:Get full text
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Summary:We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with discrete-time reinforcement learning (RL) with function approximation. We establish high-order numerical accuracy as well as the approximation error guarantees for the proposed approach. In contrast to discrete-time RL problems where the approximation factor depends on the effective horizon, we obtain a bounded approximation factor using the underlying elliptic structures, even if the effective horizon diverges to infinity.
ISSN:2331-8422