## 7 Analysis  
To validate the advantages of the multi-modal-MAPPO algorithm in multi-modal dynamic environments, this section analyzes its convergence and final performance through comparative experiments. First, Figure 4(a) presents the reward training curves of the three algorithms, showing that their rewards gradually converge as training progresses. The multi-modal-MAPPO algorithm achieves the highest reward, while MAPPO attains suboptimal performance, demonstrating that the agents can effectively learn and perceive changes in the dynamic system. Compared to MAPPO, multi-modal-MAPPO not only achieves higher rewards but also exhibits faster convergence speed and lower standard deviation, indicating a more stable training process. This validates that the introduced multi-modal dynamic attention mechanism enables the refined fusion of image-attribute features, capturing strong correlations between user demands and network states to generate high-value decisions. In contrast, MAPPO's lack of multi-modal feature interaction limits its adaptability to partially observable scenarios, resulting in constrained long-term gains. Figure 5: Training reward values and delay representations. The evaluation results presented in Figure 4(b) demonstrate the superiority of the intelligent push algorithm framework in reducing content delivery delays. By leveraging predictive capabilities for user demands and network states, both multi-modal-MAPPO and MAPPO achieve significant latency improvements over the MAAC baseline. Specifically, multi-modal-MAPPO demonstrates the lowest average delay of approximately 0.086 s, showing a 53.55% reduction compared to MAAC, while MAPPO achieves 0.1321s with a 29.55% decrease. These findings underscore the effectiveness of the proposed multi-modal architecture in optimizing proactive content caching strategies. To analyze system adaptability under varying operational conditions, we conducted parametric studies on cache capacities and user loads. As visualized in Figure 5(a), increasing cache sizes from 2000 MB to 4500 MB universally reduces delivery delays due to improved content availability. Notably, multi-modal-MAPPO maintains consistently superior performance, achieving sub-0.1 s latency across all configurations. At the minimum cache capacity of 2000 MB, it outperforms MAPPO by 0.053 s and MAAC by 0.116 s. The scalability of the proposed algorithm is further validated in Figure 5(b), where multi-modal-MAPPO achieves the lowest delays under all tested user counts (up to 18 users), demonstrating 23.17% and 38.58% improvements over MAPPO and MAAC, respectively. These results confirm the algorithm's robustness in dynamic environments. Real-time implementation feasibility is verified through Table 3, which shows the decision-making overhead of multi-modal-MAPPO (0.08654 s per decision) meets operational requirements for remote satellite caching systems. Proactive caching effectiveness is further evaluated using the push hit rates in Figure 7. Multi-modal-MAPPO achieves the highest hit rate of 0.7148, surpassing MAPPO (0.543) by 0.1718 and MAAC (0.29) by 0.4248. This substantial improvement highlights the algorithm's enhanced ability to accurately predict user demands. The learning dynamics analysis in Figure 8 reveals critical insights into parameter optimization. While a high critic learning rate (e.g., \(lr_{c}=1\times 10^{-3}\)) accelerates the initial convergence, it risks suboptimal final performance. Conversely, dual low learning rates (\(lr_{a}=1\times 10^{-4}\), \(lr_{c}=1\times 10^{-4}\)) yield slower initial progress but achieve better ultimate delays. Notably, maintaining \(lr_{c}>lr_{a}\) improves the convergence efficiency, as can be seen in the \(lr_{a}=1\times 10^{-4}\), \(lr_{c}=5\times 10^{-4}\) configuration. Inverting this ratio (e.g., \(lr_{a}=5\times 10^{-4}\), \(lr_{c}=1\times 10^{-4}\)) causes training instability and degraded performance. These findings provide valuable guidelines for balancing exploration-exploitation trade-offs in reinforcement learning-based caching systems.