## 1 Introduction
In such unpredictable and dynamic scenarios, deep reinforcement learning (DRL) has emerged as a promising alternative [13]. Unlike model-based methods, DRL employs a model-free approach, enabling agents to learn optimal actions through interactions with the environment without prior knowledge. This capability is particularly valuable in HSR MEC environments, where task occurrences and MECS load states are inherently uncertain. Furthermore, DRL optimizes long-term rewards, ensuring continuous improvement even under heavy task loads [14]. By learning complex and nonlinear patterns of task occurrence, DRL enhances resource management policies, maximizing the efficient utilization of MEC resources while maintaining QoS. Ref. [15] addressed complex resource optimization problems in vehicular environments by utilizing the Deep Deterministic Policy Gradient (DDPG) algorithm, a technique within the deep reinforcement learning (DRL) paradigm. Their study focused on optimizing the allocation of spectrum, computing, and storage resources to meet the quality of service (QoS) requirements of various vehicular applications. However, a notable limitation of their centralized approach is the significant increase in computational complexity as the number of vehicles or system scale grows. Similarly, ref. [16] proposed a DDPG-based method for optimizing task offloading decisions, with the objective of minimizing delay and optimizing computational resource usage. This centralized method also faced challenges in scalability and computational overhead in environments with a large number of vehicles or dynamic conditions. In contrast, ref. [17] adopted the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm to enable optimal task offloading in a dynamic vehicular environment where mobility and communication conditions change over time. By leveraging a distributed approach, their study effectively allocated resources to minimize delay and energy consumption. Unlike centralized approaches, distributed strategies allow for local data processing, which significantly reduces delay times and enhances scalability by distributing computational demands across multiple MEC servers (MECSs). In the context of task offloading, centralized approaches offer advantages such as global optimization and simplified management; however, they are less suitable for real-time applications due to inherent delays caused by central server communication. Furthermore, performance can degrade in large-scale networks where centralized processing becomes a bottleneck. Distributed approaches, on the other hand, process tasks locally, enabling faster response times and greater scalability, as resource allocation occurs independently at each MECS. The HSR-MEC environment presents additional challenges compared to conventional MEC-based vehicular systems due to the significantly higher speeds of high-speed trains (HSTs), which exacerbate issues such as frequent handovers and Doppler effects. Additionally, the high passenger density in HSR environments leads to increased demand for communication and computational resources. Ref. [18] explored task migration to maintain uninterrupted services in high-mobility HSR scenarios. Their work, which used DDPG for task offloading and resource allocation, focused on optimizing the task success rate but was limited by a singular optimization goal. Ref. [19] proposed a solution to optimize task execution delays by integrating a caching framework that enhances computational resource stability and network performance. Furthermore, ref. [20] combined Deep Double Q-learning (DDQN) and DDPG to improve both energy consumption and delay, employing two DRL methods to determine task offloading ratios and resource allocation decisions. This paper addresses a scenario where multiple HSTs traverse the HSR network, creating highly dynamic and complex environments. Managing all HSTs through a centralized approach is impractical due to the system's scale and variability.