# Balancing Depth for Robustness: A Study on Reincarnating Reinforcement Learning Models
## 1 Introduction  
Reinforcement learning (RL) is an important machine learning method that uses intelligent agents to learn strategies to maximize cumulative rewards through trial and error in an environment [1]. However, traditional RL methods often rely on table lookup or simple function approximation, which is not scalable enough in high-dimensional and complex tasks. To address this problem, deep reinforcement learning (DRL) uses deep neural networks to process complex states [2], which significantly improves performance, but its training process is still resource-intensive and difficult to achieve effective knowledge transfer. To solve this problem, [PERSON] et al. formally proposed a research paradigm called recurrent reinforcement learning (RRL), which aims to accelerate the new learning process by reusing existing computational results and training experience [3]. Reincarnating reinforcement learning has similarities with traditional transfer learning [4] and meta-learning [5], but its uniqueness lies in its focus on how to effectively utilize the computational results of previous models so that they can quickly adapt and continue to optimize when faced with new tasks. This method is particularly suitable for use in resource-constrained environments and can significantly reduce the computational cost of retraining models [6]. Therefore, exploring how to further improve the performance and robustness of the model in RRL has become an important direction of current research. In reinforcement learning models, deep neural networks (DNNs) play a core role as approximators of policy and value functions [7]. The structural design of deep neural networks, especially the depth of the network, directly affects the performance of the model. Traditional research shows that increasing the depth of the network can improvethe expressiveness of the model and enable the model to fit more complex functions [8]. However, excessive network expansion may also lead to overfitting problems and reduce the generalization ability of the model. The dropout technique can effectively prevent overfitting of deep networks [9]. The exploration of the robustness of Reinforcement Learning (RL) networks has garnered significant interest, driven by the urgent need for agents to reliably perform under various conditions [10]. The influence of different neural network depths has been studied from the perspective of the universal approximation theorem [11; 12], as well as functional expressivity [13]. Research on the hierarchical training of deep linear networks based on Block Coordinate Gradient Descent (BCGD) has also been conducted, with convergence analyses establishing optimal learning rates and examining the effects of depth and initialization on training [14]. In addition, studies have found that the skip connection operation used in WRN can improve the robustness of deeper architectures [15]. On the other hand, there have also been studies showing that increasing the number of parameters of the same type of deep neural network architecture can only lead to limited robustness improvements [16; 17]; wider networks may lead to more perturbation instabilities [18]. The impact of network depth on the robustness of trained DNNs challenges the belief that more parameters always enhance robustness, indicating the existence of an optimal configuration for adversarial robustness [19]. Investigations into how variations in network depth influence hidden representations have revealed block structures in large models that emerge due to over-parameterization relative to the training set size [20]. Previous empirical work has examined the effects of width and depth on model accuracy in the context of Convolutional Neural Network (CNN) architecture design, finding that optimal accuracy is often achieved by balancing width and depth [21; 22]. Further study of accuracy and error sets has been conducted in [23] (error sets over training) and [24] (error after pruning).