## 1 Introduction  
With the wide spread of mobile communication technologies, the demand for ubiquitous network access is increasing significantly. The development of industrial application in remote areas urgently requires the support of communication networks, for example, the transmission of extraction information during combustible ice extraction in offshore regions and the transmission of mechanical drawings for aircraft parts manufacturing in desert areas. However, geographic limitations make the deployment of traditional base station equipment difficult, failing to meet the communication requirements of offshore and remote industrial production [1]. Satellite communication systems, as a crucial branch of modern communication technology, establish seamless global connectivity networks with unique advantages [2, 3]. The wide coverage of satellite systems makes them ideal solutions to fill the coverage gaps of ground networks and promote global interconnectivity. Compared to geostationary orbit (GEO) and medium-Earth-orbit (MEO) satellites, low-Earth-orbit (LEO) satellites enjoy shorter communication distances and thus have the potential to meet the latency and reliability requirements of industrial applications [4]. Due to the uneven geographical distribution of user equipments and the diversity in their communication demands, effectively scheduling limited LEO satellite resourcesto meet the communication needs of user equipments is a significant challenge. Traditional static single-beam satellite resource allocation strategies lack flexibility, making it difficult to address the diverse requirements of industrial applications, resulting in low resource utilization and poor communication quality. Multi-beam satellites, leveraging beam-hopping technology, can flexibly allocate beams and frequency resources within each time slot to serve users in different regions, which enables efficient utilization of on-board resources [5; 6; 7]. Furthermore, multi-beam satellites can achieve robust interference management through minimizing inter-beam interference with strategic beam planning and precise spectrum management [8]. Due to the limited on-board resources and the diverse needs of users, it is urgent to develop a resource allocation strategy that enhances resource utilization and communication efficiency while coordinating interference. In recent years, some studies have focused on the efficient allocation of limited resources on LEO satellites to enhance the performance of satellite-to-ground link transmissions. In [9], [PERSON] et al. design an uplink resource allocation strategy for a narrowband Internet of Things (IoT) system on LEO satellites, which takes into account the varying channel conditions of the satellite and the data transmission requirements of user equipments. In [10], [PERSON] et al. propose a beam-hopping resource allocation strategy for scenarios with overlapping coverage by multiple LEO satellites. This scheme considers both inter-satellite and intra-satellite interference during beam-hopping scheduling and communication tasks and effectively minimizes the total transmission time. With the booming development of artificial intelligence (AI) and deep neural networks (DNNs), some multi-beam satellite resource allocation schemes based on deep reinforcement learning (DRL) have also been proposed. In [11], [PERSON] et al. consider a joint optimization problem of resource allocation and power control in a LEO satellite-ground network based on rate-splitting multiple access (RSMA). To address the challenge of continuous power control and discrete resource allocation under limited system information, the authors propose a framework based on DRL, which employs the deep Q-network (DQN) algorithm for discrete resource allocation and the proximal policy optimization (PPO) algorithm for continuous power control, aiming to maximize the joint objective. To better address the uneven and time-varying nature of ground communication service requests, [PERSON] et al.