## 1 Introduction  
At present, due to resource constraints, including limitations regarding computing and storage, user nodes (UNs) with miniaturized designs cannot locally process large amounts of perceptual data. In a cloud architecture, the original data needs to be transmitted to a remote cloud computing platform for calculation. However, transferring large volumes of raw data to the remote platform results in significant energy consumption overhead for UNs. As an auxiliary technology for cloud computing, edge computing can effectively address the energy constraints of UNs by optimizing information processing and transmission. Consequently, cloudlets [1] and edge computing [2] have been extensively researched. Although edge computing can decrease the energy consumption rate of UNs, it cannot solve the fundamental problem of the limited UN battery lifetime. Currently, batteries are the primary power source for UNs. However, these batteries have limited energy capacities and can be difficult to replace in certain environments. To address the issue of energy limitations, there has been an increasing amount of research into wireless power supplies. In terms of energy source selection, traditional sources like solar, wind, and other energy resources are significantly affected by geographic and environmental factors. Extensive research has been conducted on the collection of energy from wireless spectrum signals,as these signals represent a controllable and predictable energy source [3]. Additionally, wireless signals can serve both as a source of energy and as a carrier for information transmission. In the process of wireless energy harvesting, the amount of energy collected by UNs depends on the channel quality. More energy can be collected when the UN is closer to an access point (AP), enabling it to transmit more data. Conversely, a UN farther from the AP collects less energy. As a result, tasks that need to be offloaded to a mobile edge computing (MEC) server may experience delays because of insufficient energy. This phenomenon is known as the \"near-far\" effect. By integrating an energy supply network into MEC, computationally intensive tasks can be offloaded to nearby edge servers or UNs, reducing power consumption and computational latency [4; 5]. This paper studied a wireless powered mobile edge computing (WPMEC) scenario where UNs complete latency-critical, computation-intensive tasks offloaded to an edge server through cooperative communication, with all UN energy supplied entirely by the AP. A method was designed to determine the data forwarding path, the amount of data to forward, and the energy harvesting time to ensure that all the UN tasks reach the AP as quickly as possible, while minimizing the system delay. First, the problem of minimizing delay was formalized as a mixed nonlinear integer programming (MINLP) problem. Given that this problem is NP-hard, a delay-optimal approximation algorithm (DOPA) was proposed. Finally, a deep learning-based online offloading (DLOO) framework was designed to predict the transmission power of each UN in the WPMEC. Compared to existing methods for solving the WPMEC optimization problem, this paper makes the following contributions:  
1. To eliminate the \"near-far\" effect in the WPMEC, a UN cooperative transmission method is introduced. This method improves the data offloading delay of \"far\" UNs by enabling UN cooperation, while also eliminating the deployment cost of relay nodes. 2. In the case of energy-constrained edge computing, a proposal is made to transfer tasks that need to be offloaded to the MEC server as quickly as possible. A mathematical model aimed at minimum delay is established and solved using the proposed DOPA method to reduce the data offloading delay. 3. The proposed DLOO framework draws lessons from historical experiences under various wireless channel conditions and automatically predicts the transmission power of the UNs. This approach significantly reduces calculation delay while ensuring accurate predictions.