## 1 Introduction
When the network topology changes, the original routing decisions may no longer be applicable to the new topology. For example, changes in link conditions, node failures, or the addition of new devices can cause the original routing decisions to degrade in performance or become inapplicable. At this point, the routing algorithm based on reinforcement learning needs to re-collect the current network status, retrain, and update routing decisions accordingly. This process allows the algorithm to adapt to the new network environment and maintain efficient routing decision-making capabilities, thereby avoiding performance loss [6]. Currently, researchers have conducted research on routing algorithms based on reinforcement learning and proposed a series of intelligent routing algorithm solutions. [PERSON] et al. [7] proposed a multi-agent reinforcement learning method for inter-domain routing, which improved the overall performance of the network. [PERSON] et al. [8] used a comprehensive reward function, an efficient learning algorithm, and a novel deep neural network structure to learn appropriate routing strategies for different types of traffic demands. [PERSON] et al. [6] constructed a routing reinforcement learning strategy that can operate in dynamic network conditions without retraining and compared this method with other routing protocols on various quality of service indicators. [PERSON] et al. [9] proposed Deep CQ+ routing, which integrates the emerging multi-agent deep reinforcement learning technology into the existing Q-learning-based routing protocol and achieves consistently higher performance across a wide range of network topologies, demonstrating a high degree of robustness and scalability. [PERSON] et al. [10] proposed a packet routing framework based on multi-agent deep reinforcement learning, which performs training and decision-making in a fully distributed environment, effectively approximates the value function of Q learning, and reduces the transmission time of packets. [PERSON] et al. [11] used deep reinforcement learning to select routers in large-volume networks, reducing network congestion and data transmission paths, and used Markov decision processes to formulate routing problems. They designed two novel Deep Q Network (DQN)-based algorithms to reduce the probability of network congestion with shorter transmission paths. [PERSON] et al. [12] proposed an effective solution to the routing optimization problem by integrating a Graph Neural Network (GNN) structure into DRL; the characteristics of GNN are used to interact with the network topology environment. Through the message-passing process of information exchange between links in the topology, available knowledge is extracted to achieve network traffic load balancing, and network performance is enhanced. [PERSON] et al. [13] proposed a deep reinforcement learning-based routing optimization model framework, SINET, which achieves intelligent optimization of network routing by controlling some key nodes. [PERSON] et al. [14] proposed a scalable inter-domain multi-link routing optimization mechanism based on multi-agent reinforcement learning. The proposed mechanism dynamically adjusts inter-domain link routing by real-time sensing of traffic distribution, maximizing throughput across autonomous systems. At present, most existing elastic routing algorithms (e.g., single-agent DRL-based methods) can improve network performance under static topology, but they lack the ability to efficiently re-converge to optimal routing decisions when facing dynamic topology changes. In contrast, the ERA-MADDPG algorithm proposed in this paper introduces multi-agent collaborative learning to enhance the 'elasticity' of routing, defined as the capability to rapidly adapt to topology changes through real-time policy updates and inter-agent knowledge sharing.