## 1 Introduction  
Multimodal large language models (MLLMs) powered by transformer architectures represent a breakthrough in artificial intelligence, fundamentally differing from ordinary AI optimization algorithms such as traditional machine learning models or heuristic optimization techniques. While conventional AI models typically process single-modality data with limited computational complexity, MLLMs integrate diverse data modalities for advanced pattern recognition and contextually rich output generation. However, this advanced functionality comes at the cost of massive computational requirements, often billions of parameters, making their deployment particularly challenging. The prevalent cloud-based deployment model introduces critical bottlenecks: prohibitive latency for real-time applications and excessive bandwidth consumption for multimodal data transmission [1]. These limitations are particularly acute in IoT environments where edge devices possess minimal computational capacity, creating an urgent need for distributed computing solutions specifically designed for MLLMs. Mobile edge computing (MEC) emerged as a promising solution by bringing computational resources closer to data sources [2; 3; 4]. However, as IoT applications expand into remote terrestrial and maritime environments, areas crucial for applications like offshore monitoring and disaster response, traditional cellular-based MEC faces fundamental coverage limitations [5]. The prohibitive costs of infrastructure deployment in these regions demand alternative approaches. This gap has catalyzed the development of satellite edge computing (SEC), which leverages low Earth orbit (LEO) satellites augmented by unmanned aerial vehicles (UAVs) to create a ubiquitous computational layer [6; 7]. UAVs serve as dynamic computing nodes that can process tasks locally, adapting their positions to optimize coverage and minimize latency, capabilities essential for supporting MLLM-based services in connectivity-challenged environments [8]. The integration of MLLMs into SEC networks unlocked unprecedented possibilities for intelligent edge applications. By enabling complex multimodal reasoning at the network edge, this paradigm supports autonomous decision-making while preserving data privacy. The key to realizing this potential lies in intelligent task distribution: determining optimal processing locations based on task characteristics, network conditions, and available resources. This requires sophisticated algorithms for task offloading and resource allocation that can navigate the trade-offs between computational capacity, communication latency, and energy constraints across heterogeneous computing nodes [9]. However, MLLM task offloading and resource allocation in SEC networks present unique challenges that far exceed traditional edge computing scenarios [10]. The massive parameter scale of MLLMs, often billions of parameters, creates extraordinary computational demands that strain the limited resources of satellite and UAV platforms [11]. Compounding this challenge, the inherent dynamics of SEC networks introduce additional complexity: LEO satellites' rapid orbital motion causes frequent topology changes, time-varying channel conditions create unpredictable communication links, and the heterogeneous nature of computing nodes, including LEO satellites and UAVs, requires coordinated resource management [12]. These factors render static optimization approaches obsolete, as they cannot adapt to the continuously evolving network state [13]. The complexity and scale of this optimization problem exceed the capabilities of conventional approaches. While dynamic programming suffers from the curse of dimensionality, heuristic methods lack performance guarantees in highly dynamic environments. Deep reinforcement learning (DRL) offers a compelling alternative, learning adaptive policies through interaction with the environment [14; 15; 16].