## 5 Performance Evaluation
### Numerical Results  
First, we analyze the convergence of the proposed AD-SAC algorithm and the comparative DRL algorithms. Figure 3 illustrates the learning curves for the AD-SAC, PPO, D3 QN, DDPG, and Hybrid-PPO algorithms across 1000 epochs. AD-SAC demonstrates superior convergence speed and performance, outperforming the benchmark algorithms. Specifically, AD-SAC reaches a significantly higher final average reward, while Hybrid \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Value** \\ \hline Number of IoTDs: \(K\) & 10 \\ \hline Number of UAVs: \(M\) & 3 \\ \hline Number of LEO satellites: \(N\) & 4 \\ \hline FLOPS used by one inference step: \(v_{m}\) & [0.05, 0.6] TFLOPS \\ \hline Noise power density: \(N_{0}\) & \(-100\,\mathrm{dBm}/\,\mathrm{Hz}\) \\ \hline Time slot: \(T\) & 100 \\ \hline Computation power of UAV & 25 W \\ \hline Computation power of LEO satellite & 50 W \\ \hline Maximum uplink transmission power of IoTD & 1 W \\ \hline Transmission power of UAV, satellite & 2 W, 4 W \\ \hline Channel bandwidth: \(B_{n}\), \(B_{m}\) & 20 MHz, 10 MHz \\ \hline Transmission rate between LEO satellites: \(R_{ISL}\) & 1 Gbps \\ \hline Input data size: \(u_{k}\) & [5.0, 10.0] Mbits \\ \hline Maximum latency requirement: \(T_{k}^{max}\) & [2.0, 3.0] s \\ \hline MMMU benchmark accuracy requirement: \(a_{k}\) & [0.3, 0.7] \\ \hline Weighted coefficients: \(\eta_{l},\eta_{c}\) & 0.5, 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameter settings. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Network type & Fully connected & Number of layers & 3 \\ \hline Hidden units & [256; 256; 256] & Activation & ReLU \\ \hline Optimizer & Adam & Entropy learning rate & 0.001 \\ \hline Actor learning rate & 0.001 & Critic learning rate & 0.001 \\ \hline Batch size & 64 & Replay buffer size & 10,000 \\ \hline Discount factor \(\gamma\) & 0.995 & Soft update \(\tau\) & 0.01 \\ \hline Training epochs & 1000 & Epoch length & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The hyperparameters of the proposed AD-SAC algorithm. PPO, DDPG, D3 QN, and PPO obtain approximately 5.7-13.4% lower reward compared to the AD-SAC algorithm. This indicates that AD-SAC not only converges faster but also maintains better stability throughout training. While Hybrid-PPO exhibits a relatively stable learning curve and a higher final reward than DDPG, D3 QN, and PPO, its performance is still notably lower than that of the AD-SAC algorithm. PPO and D3 QN, on the other hand, exhibit greater reward fluctuations and slower convergence rates, ultimately stabilizing at lower reward levels. This analysis emphasizes AD-SAC's superior stability, faster convergence, and overall effectiveness compared to the other algorithms. Figure 4 demonstrates the impact of varying the critic learning rate on the convergence behavior of the AD-SAC algorithm for MLLM task offloading in UAV-assisted SEC networks. The figure illustrates that a moderate critic learning rate facilitates rapid and stable convergence, with the average reward per episode increasing swiftly to a high plateau, indicating efficient minimization of the weighted sum of latency and energy consumption. In contrast, the lower critic learning rate with 0.0001 results in slower convergence, requiring more training episodes to achieve comparable performance, while the critic learning rate with 0.01 leads to oscillatory behavior and failure to stabilize, reflecting instability in the training process. These findings highlight the critical role of carefully tuning the critic learning rate to balance the learning speed and stability within the hybrid action space DRL framework, ensuring effective task allocation and resource management in the resource-constrained SEC environment. Therefore, in the subsequent experiments, we set the critic learning rate to 0.001 to ensure the efficiency and robustness of the AD-SAC algorithm.