Cost Minimization for Space-Air-Ground Integrated Multi-Access Edge Computing Systems

Space-air-ground integrated multi-access edge computing (SAGIN-MEC) provides a promising solution for the rapidly developing low-altitude economy (LAE) to deliver flexible and wide-area computing services. However, fully realizing the potential of SAGIN-MEC in the LAE presents significant challenges, including coordinating decisions across heterogeneous nodes with different roles, modeling complex factors such as mobility and network variability, and handling real-time decision-making under partially observable environment with hybrid variables. To address these challenges, we first present a hierarchical SAGIN-MEC architecture that enables the coordination between user devices (UDs), uncrewed aerial vehicles (UAVs), and satellites. Then, we formulate a UD cost minimization optimization problem (UCMOP) to minimize the UD cost by jointly optimizing the task offloading ratio, UAV trajectory planning, computing resource allocation, and UD association. We show that the UCMOP is an NP-hard problem. To overcome this challenge, we propose a multi-agent deep deterministic policy gradient (MADDPG)-convex optimization and coalitional game (MADDPG-COCG) algorithm. Specifically, we employ the MADDPG algorithm to optimize the continuous temporal decisions for heterogeneous nodes in the partially observable SAGIN-MEC system. Moreover, we propose a convex optimization and coalitional game (COCG) method to enhance the conventional MADDPG by deterministically handling the hybrid and varying-dimensional decisions. Simulation results demonstrate that the proposed MADDPG-COCG algorithm significantly enhances the user-centric performances in terms of the aggregated UD cost, task completion delay, and UD energy consumption, with a slight increase in UAV energy consumption, compared to the benchmark algorithms. Moreover, the MADDPG-COCG algorithm shows superior convergence stability and scalability.