Extensive utilization of deep reinforcement learning (DRL) policy networks in diverse continuous control tasks has raised questions regarding performance degradation in expansive state spaces where the input state norm is larger than that in the training environment. This paper aims to uncover the underlying factors contributing to such performance deterioration when dealing with expanded state spaces, using a novel analysis technique known as state division. In contrast to prior approaches that employ state division merely as a post-hoc explanatory tool, our methodology delves into the intrinsic characteristics of DRL policy networks. Specifically, we demonstrate that the expansion of state space induces the activation function $\tanh$ to exhibit saturability, resulting in the transformation of the state division boundary from nonlinear to linear. Our analysis centers on the paradigm of the double-integrator system, revealing that this gradual shift towards linearity imparts a control behavior reminiscent of bang-bang control. However, the inherent linearity of the division boundary prevents the attainment of an ideal bang-bang control, thereby introducing unavoidable overshooting. Our experimental investigations, employing diverse RL algorithms, establish that this performance phenomenon stems from inherent attributes of the DRL policy network, remaining consistent across various optimization algorithms.

翻译：深度强化学习策略网络在多种连续控制任务中的广泛应用，引发了关于其在输入状态范数大于训练环境的大规模状态空间中性能下降的疑问。本文旨在利用一种称为状态划分的新颖分析技术，揭示导致状态空间扩展时性能恶化的潜在因素。与以往仅将状态划分作为事后解释工具的方法不同，我们的方法深入探究了深度强化学习策略网络的内在特性。具体而言，我们证明状态空间的扩展会导致激活函数 $\tanh$ 呈现饱和性，从而使状态划分边界从非线性转变为线性。我们的分析以双积分器系统为范例，揭示了这种向线性化的逐步转变会赋予系统类似于砰-砰控制的控制行为。然而，划分边界固有的线性特性阻碍了理想砰-砰控制的实现，从而引入了不可避免的过冲现象。我们采用多种强化学习算法进行的实验研究表明，这种性能现象源于深度强化学习策略网络的内在属性，并且在各种优化算法下保持一致。