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

• URL: http://arxiv.org/abs/2407.05966v1
• Date: Mon, 8 Jul 2024 14:05:03 GMT
• Title: On Bellman equations for continuous-time policy evaluation I: discretization and approximation
• Authors: Wenlong Mou, Yuhua Zhu,
• Abstract 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.
• Score: 3.704688279256839
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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