We provide the first convergence analysis of local gradient descent for minimizing the average of smooth and convex but otherwise arbitrary functions. Problems of this form and local gradient descent as a solution method are of importance in federated learning, where each function is based on private data stored by a user on a mobile device, and the data of different users can be arbitrarily heterogeneous. We show that in a low accuracy regime, the method has the same communication complexity as gradient descent.

中文翻译：

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异构数据上局部GD的初步分析

我们提供了局部梯度下降的第一次收敛分析，以最小化平滑和凸函数的平均值，但其他任意函数。这种形式的问题和作为解决方法的局部梯度下降在联邦学习中很重要，其中每个函数都基于用户在移动设备上存储的私有数据，不同用户的数据可以任意异构。我们表明，在低准确率的情况下，该方法具有与梯度下降相同的通信复杂性。