Robust Optimization of Low-Altitude Communication and Computation Resources in Uncertain Environments
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摘要: 针对低空边缘网络中因任务数据量的突发性与无人机飞行位置抖动所引起的服务质量下降问题，该文提出一种基于分布鲁棒优化的系统能耗最小化方法。首先，综合考虑任务大小和飞行位置不确定性因素，建立以最小化系统加权总能耗为目标的网络模型，并对无人机飞行轨迹、任务划分以及计算与通信资源进行协同设计。其次，将该非凸且复杂的优化问题建模为马尔可夫决策过程，并提出基于分布鲁棒优化的软演员-评论家算法。该算法通过构建任务需求分布的模糊集以处理分布不确定性，并借助最大熵强化学习框架，在连续动作空间中求解最坏概率分布下的最优策略。仿真结果表明，所提算法在动态环境中具有更快的收敛速度，且在不同任务负载及位置扰动下均能显著降低系统加权能耗，其中用户和无人机能耗分别降低了21.1%和15.9%。Abstract:
Objective Low-altitude edge computing network is utilized to provide flexible computing services and enhance coverage for user equipment. However, the quality of service is often compromised by the significant uncertainty in task data sizes and the inevitable position jitter of UAVs caused by environmental disturbances. Existing robust solutions typically rely on deterministic uncertainty sets, which are often too conservative to accurately capture the stochastic nature of task demands. To address these challenges, a robust energy minimization framework is proposed for multi-UAV MEC networks. The primary objective is to minimize the weighted sum of system energy consumption. This is achieved by establishing a joint optimization model that coordinates UAV flight trajectories, task splitting decisions, and the allocation of computation and communication resources, explicitly accounting for the dual uncertainties of task magnitude and flight positioning. Methods To address the non-convexity and high coupling of the optimization variables, the problem is first modeled as a Markov Decision Process (MDP). A comprehensive state space is defined to characterize real-time system dynamics, while a continuous action space is designed for trajectory control and resource management. A Distributionally Robust Optimization Soft Actor-Critic (DRO-SAC) algorithm is developed to solve this MDP. Within this framework, an ambiguity set is constructed based on the L1-norm distance to characterize the distributional uncertainty of task demands. A maximum entropy reinforcement learning mechanism is then employed to learn the optimal policy against the worst-case distribution within the ambiguity set. Through this approach, UAV trajectories and power allocation are jointly optimized to ensure system robustness against dynamic environmental fluctuations. Results and Discussions The performance of the proposed DRO-SAC algorithm is evaluated through simulation experiments. It is observed that DRO-SAC achieves faster convergence and higher rewards compared to DDPG and PPO ( Fig. 3 ). In terms of energy consumption, superior efficiency is consistently demonstrated by the proposed method under varying user densities (Fig. 4 ). Furthermore, the system's robustness against position errors is verified, with energy fluctuations maintained at a low level (Fig. 5 ). Finally, dynamic trajectory adjustments are visualized, confirming effective user coverage and energy minimization (Fig. 6 ).Conclusions A joint optimization framework based on DRO-SAC is proposed in this paper to address the uncertainties of task data size and UAV flight jitter in multi-UAV assisted MEC networks. By constructing an ambiguity set for task demand distribution and optimizing the worst-case expected objective, the limitations of traditional deterministic models in dynamic environments are effectively overcome. The weighted system energy consumption is minimized while satisfying latency and safety constraints. Finally, the superior convergence stability and energy efficiency of the proposed scheme are demonstrated through simulation results, even under conditions of limited resources and severe environmental fluctuations. -
1 本文提出的DRO-SAC算法
(1) 建立经验回放池$ {\mathcal{R}} $，初始化网络参数 (2) 对每个训练周期执行： (3) 对每个环境交互步骤执行： (4) 根据策略分布$ {\text{π} }_{\phi }({a}_{l}|{s}_{l}) $采样动作$ {a}_{l} $ (5) 构建不确定性集合$ {D}_{i} $，选择分布$ {{\mathbb{P}}}_{i} $ (6) 获得奖励$ {r}_{l} $，并观测下一状态$ {s}_{l+1} $ (7) 将状态转移元组$ ({s}_{l},{a}_{l},{r}_{l},{s}_{l+1}) $存入经验回放池$ {\mathcal{R}} $ (8) 对每个梯度更新步骤执行： (9) 从$ {\mathcal{R}} $中随机采样一批经验样本 (10) 优化评论家网络：$ {\theta }_{k}\leftarrow {\nabla }_{{{\theta }_{k}}}{J}_{Q}({\theta }_{k}),k\in \{1,2\} $ (11) 更新策略网络：$ \phi \leftarrow {\nabla }_{\phi }{J}_{\text{π} }(\phi ) $ (12) 对目标网络进行软更新：$ {\overline{\theta }}_{k}\leftarrow \varsigma {\theta }_{k}+(1-\varsigma ){\overline{\theta }}_{k},k\in \{1,2\} $ 
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表 1 参数设置
参数 设置 参数 设置 桨叶叶尖速度$ {U}_{\text{tip}} $ 120 m/s 无人机飞行高度$ H $ 150 m 叶片功率$ {P}_{1} $ 59.03 W 无人机最小安全距离$ {d}_{\text{dim}} $ 3 m 悬停功率$ {P}_{2} $ 79.07 W 最大发射功率$ {p}_{i,\text{max}} $ 0.5 W 旋翼速度$ {V}_{0} $ 3.6 m/s 无人机最大计算能力$ f_{u}^{\text{max}} $ 10 GHz 旋翼面积$ {A}_{0} $ 0.5030 m2用户最大计算能力$ f_{i}^{\text{max}} $ 1 GHz 无人机最大飞行速度$ {v}_{\text{max}} $ 35 m/s 信道高斯白噪声功率$ {\sigma }^{2} $ -85 dBm 信道带宽$ B $ 10 MHz 无人机最大服务用户上限$ {M}_{\max } $ 8
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