论文标题
关于梯度跟踪和本地更新的性能
On the Performance of Gradient Tracking with Local Updates
论文作者
论文摘要
我们研究了分散的优化问题,其中$ n $代理的网络试图最大程度地降低一组异质非凸成本功能的平均值。最新的分散算法(例如精确扩散〜(ED)和梯度跟踪〜(GT))涉及传达每一个迭代。但是,沟通昂贵,资源密集且缓慢。在这项工作中,我们分析了当地更新的GT方法(LU-GT),在该方法与邻居互动之前,代理在该方法进行本地递归。尽管已显示本地更新可以减少实践中的沟通开销,但其理论影响尚未完全表征。我们显示Lu-GT与联合学习设置具有相同的通信复杂性,但允许任意网络拓扑。此外,我们证明本地更新的数量不会降低LU-GT实现的解决方案的质量。数值示例表明,本地更新可以降低某些制度中的通信成本(例如,连接良好的图形)。
We study the decentralized optimization problem where a network of $n$ agents seeks to minimize the average of a set of heterogeneous non-convex cost functions distributedly. State-of-the-art decentralized algorithms like Exact Diffusion~(ED) and Gradient Tracking~(GT) involve communicating every iteration. However, communication is expensive, resource intensive, and slow. In this work, we analyze a locally updated GT method (LU-GT), where agents perform local recursions before interacting with their neighbors. While local updates have been shown to reduce communication overhead in practice, their theoretical influence has not been fully characterized. We show LU-GT has the same communication complexity as the Federated Learning setting but allows arbitrary network topologies. In addition, we prove that the number of local updates does not degrade the quality of the solution achieved by LU-GT. Numerical examples reveal that local updates can lower communication costs in certain regimes (e.g., well-connected graphs).