采用加速梯度法的集中式网络效用最大化
Centralized Network Utility Maximization with Accelerated Gradient Method
AI总结：
本文针对SDN场景下集中式网络效用最大化研究忽略效率的问题，通过构造光滑目标函数应用Nesterov加速梯度法，提出兼具效率与流量维度可扩展性的算法，实现$O(d/t^2)$收敛速率与接近最优的效用。
摘要：
网络效用最大化（NUM）是网络流量管理与资源分配领域的一个已被广泛研究的问题。由于网络固有的分布式特性与复杂性，大多数研究都聚焦于开发分布式NUM算法。近年来，软件定义网络（SDN）架构得到了广泛应用，尤其是在大型企业管理的云网络和数据中心互联网络中，这推动了集中式NUM算法的设计。为应对此类SDN网络中流量规模庞大且持续增长的问题，现有集中式NUM相关研究主要关注算法在流量数量维度上的可扩展性，却忽略了效率问题。本文聚焦SDN场景，针对NUM问题推导了一种集中式、高效且具备可扩展性的算法。通过设计光滑效用函数与光滑惩罚函数，我们将NUM问题转化为具有光滑目标函数的形式，从而得以应用Nesterov加速梯度法。我们证明了所提方法具有$O(d/t^2)$的收敛速率，这在迭代次数$t$维度上是最快的，且该方法在网络中流量数量$d$维度上具备可扩展性。实验表明，我们的方法能用更少的迭代次数得到精确解，并实现接近最优的网络效用。
英文摘要：
Network utility maximization (NUM) is a well-studied problem for network traffic management and resource allocation. Because of the inherent decentralization and complexity of networks, most researches develop decentralized NUM algorithms. In recent years, the Software Defined Networking (SDN) architecture has been widely used, especially in cloud networks and inter-datacenter networks managed by large enterprises, promoting the design of centralized NUM algorithms. To cope with the large and increasing number of flows in such SDN networks, existing researches about centralized NUM focus on the scalability of the algorithm with respect to the number of flows, however the efficiency is ignored. In this paper, we focus on the SDN scenario, and derive a centralized, efficient and scalable algorithm for the NUM problem. By the designing of a smooth utility function and a smooth penalty function, we formulate the NUM problem with a smooth objective function, which enables the use of Nesterov's accelerated gradient method. We prove that the proposed method has $O(d/t^2)$ convergence rate, which is the fastest with respect to the number of iterations $t$, and our method is scalable with respect to the number of flows $d$ in the network. Experiments show that our method obtains accurate solutions with less iterations, and achieves close-to-optimal network utility.
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