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

Wenlong Mou; Yuhua Zhu

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arXiv · 2407.05966

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

Wenlong Mou·Yuhua Zhu

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Abstract

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.

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Wenlong Mou, Yuhua Zhu. 2024-07-08. On Bellman equations for continuous-time policy evaluation I: discretization and approximation. https://arxiv.org/abs/2407.05966

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