Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time control problems, is unable to directly estimate the generalization error of the Bellman optimal loss and require a boundedness assumption. Our work focuses on continuous-time control problems and proposes a method that is applicable to all such problems where the transition function satisfies semi-group and Lipschitz properties. Under this method, we can directly analyze the \emph{a priori} generalization error of the Bellman optimal loss. The core of this method lies in two transformations of the loss function. To complete the transformation, we propose a decomposition method for the maximum operator. Additionally, this analysis method does not require a boundedness assumption. Finally, we obtain an \emph{a priori} generalization error without the curse of dimensionality.

翻译：深度强化学习在众多大规模实际应用中表现出色。然而，现有性能分析忽略了连续时间控制问题的独特性，无法直接估计贝尔曼最优损失的泛化误差，且需要有界性假设。本研究聚焦于连续时间控制问题，提出了一种适用于所有转移函数满足半群和利普希茨性质的此类问题的方法。在该方法下，我们可以直接分析贝尔曼最优损失的先验泛化误差。该方法的核心在于对损失函数进行两次变换。为完成变换，我们提出了一种针对最大算子的分解方法。此外，该分析方法无需有界性假设。最终，我们得到了一个无维度灾难的先验泛化误差。