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arXiv 2007.00878cs.LGmath.OCstat.ML
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局部更新方法中学习率的超常重要性

On the Outsized Importance of Learning Rates in Local Update Methods

Google Research(谷歌研究院)

Zachary Charles, Jakub Konečný

摘要:

我们研究了一系列算法,我们称之为局部更新方法,它概括了许多联邦学习和元学习算法。我们证明,二次目标,局部更新方法执行随机梯度下降的代理损失函数,我们确切地描述。我们发现,客户端学习率的选择控制的条件数,代理损失,以及代理和真正的损失函数的最小值之间的距离。我们使用这个理论,以获得新的联邦平均的收敛速度,展示这种替代损失的条件数和它的对齐与真正的损失函数之间的权衡。我们验证我们的研究结果经验,表明在通信有限的设置,适当的学习率调整往往足以达到接近最佳的行为。我们还提出了一种实用的方法,用于本地更新方法中的自动学习率衰减,这有助于减少对学习率调整的需求,并突出了其在各种任务和数据集上的经验性能。

英文摘要:

We study a family of algorithms, which we refer to as local update methods, that generalize many federated learning and meta-learning algorithms. We prove that for quadratic objectives, local update methods perform stochastic gradient descent on a surrogate loss function which we exactly characterize. We show that the choice of client learning rate controls the condition number of that surrogate loss, as well as the distance between the minimizers of the surrogate and true loss functions. We use this theory to derive novel convergence rates for federated averaging that showcase this trade-off between the condition number of the surrogate loss and its alignment with the true loss function. We validate our results empirically, showing that in communication-limited settings, proper learning rate tuning is often sufficient to reach near-optimal behavior. We also present a practical method for automatic learning rate decay in local update methods that helps reduce the need for learning rate tuning, and highlight its empirical performance on a variety of tasks and datasets.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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