## 1 Introduction  
With the advancement of 5G and next-generation networks, the MEC (Multi-access Edge Computing) system is gaining attention [1, 2]. MEC provides the advantage of significantly reducing latency by processing data at the network edge close to users rather than in a central cloud, which makes it ideal for services requiring real-time response. Applications such as autonomous driving [3], augmented reality [4], virtual reality [5], and the industrial Internet of Things (IoT) [6] require low latency and high processing speeds, which establish MEC as an essential technology for these purposes [7]. However, with the proliferation of MEC servers (MECSs), energy consumption issues are emerging. MEC systems deploy multiple MECSs at the network edge to accommodate user demand during peak hours. However, during off-peak hours, the utilization of these MECSs significantly decreases. Even when servers are not processing tasks, they consume a considerable amount of energy. Therefore, when the workload is low relative to the overall system capacity, operating an unnecessarily large number of MEC servers in an active state leads to increased energy consumption, which causes increased operational costs and environmental impacts [8, 9]. Consequently, research efforts are underway to improve the energy efficiency of the MEC system. In particular, dynamically switching the operational status of MECSs between active and sleep states according to the MEC system's workload is emerging as one of the key methods for energy conservation [10]. Keeping all MEC servers running constantly can lead to energy waste, and energy savings can be achieved by turning off unnecessary MECSs. However, when MECSs are turned off, there may be deterioration in QoS (Quality of Service) that the system provides, especially in terms of latency, when processing user tasks. Therefore, a strategy is needed that ensures energy savings while guaranteeing acceptable service latency levels for users. However, task offloading patterns in the MEC system fluctuate irregularly due to both the mobility of mobile users and the spatio-temporal variations in their service usage patterns. Consequently, it becomes challenging to accurately predict task workloads that vary across different times and locations, and any errors in such predictions can trigger erroneous server state transitions [11]. In addition, the time taken for deciding MECS operational state is crucial [12]. If the transition time from active to sleep state is too late, it results in energy waste, while the late transition from sleep to active can increase the service delay. Determining the optimal operational state of each MECS in the system requires consideration of multidimensional system state information, including per-server load levels, user distribution patterns, and the spatial distribution of generated workloads. Moreover, these state transition decisions must be made continuously in an environment where such complex state information changes in real-time. Therefore, there is a critical need to develop an efficient MECS operational state management technique that can make fast and accurate state transition decisions by effectively utilizing this complex system state information. In the meantime, due to their outstanding generalization and function approximation capabilities, deep learning techniques are being extensively applied to classification and prediction problems, including image and speech recognition and synthesis, as well as video and text generation [13; 14]. Following the demonstrated effectiveness of this methodology, research efforts are actively exploring the application of deep learning technologies to dynamically optimize the performance of mobile communication systems and computing systems. As an integral component of these extensive research endeavors, we introduce a deep learning-based approach to address the challenges of MECS operational state management.