基于双变量回归的无线资源分配快速状态增强学习
Fast State-Augmented Learning for Wireless Resource Allocation with Dual Variable Regression
- Department of Electrical and Systems Engineering, University of Pennsylvania（宾夕法尼亚大学电气与系统工程系）
- Department of Biostatistics and Bioinformatics, Duke University（杜克大学生物统计与生物信息学系）
- Johns Hopkins Applied Research Laboratory (APL)（约翰霍普金斯应用研究实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究多用户无线网络资源分配问题，提出基于状态增强图神经网络的方法，利用双变量回归实现对偶乘数近最优初始化加快推理，通过最大化拉格朗日函数改善模型训练，经实验验证算法性能优越并给出收敛结果和概率界。
AI中文摘要：
我们考虑多用户无线网络中的资源分配问题，目标是在用户遍历平均性能约束下优化网络范围的效用函数。我们展示了一种用于资源分配策略的状态增强图神经网络（GNN）参数化方法如何克服普遍存在的双次梯度方法的缺点，即将网络配置（或状态）表示为图，并将对偶变量视为模型的动态输入，当作图上支持的图信号。在离线训练阶段学习拉格朗日最大化状态增强策略，在推理阶段执行学习到的状态增强策略时，对偶变量通过梯度更新演变。我们的主要贡献在于说明如何利用辅助GNN参数化通过双变量回归实现对偶乘数的近最优初始化以加快推理，以及如何在从对偶下降动态采样的乘数上最大化拉格朗日函数以显著改善状态增强模型的训练。我们在发射功率控制的案例研究中通过大量数值实验证明了所提算法的优越性能。最后，我们证明了对偶函数（迭代）最优性差距的收敛结果和指数概率界。
英文摘要：
We consider resource allocation problems in multi-user wireless networks, where the goal is to optimize a network-wide utility function subject to constraints on the ergodic average performance of users. We demonstrate how a state-augmented graph neural network (GNN) parametrization for the resource allocation policy circumvents the drawbacks of the ubiquitous dual subgradient methods by representing the network configurations (or states) as graphs and viewing dual variables as dynamic inputs to the model, treated as graph signals supported over the graphs. Lagrangian maximizing state-augmented policies are learned during the offline training phase, and the dual variables evolve through gradient updates while executing the learned state-augmented policies during the inference phase. Our main contributions are to illustrate how near-optimal initialization of dual multipliers for faster inference can be accomplished with dual variable regression, leveraging a secondary GNN parametrization, and how maximization of the Lagrangian over the multipliers sampled from the dual descent dynamics substantially improves the training of state-augmented models. We demonstrate the superior performance of the proposed algorithm with extensive numerical experiments in a case study of transmit power control. Finally, we prove a convergence result and an exponential probability bound on the excursions of the dual function (iterate) optimality gaps.
