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On the Outsized Importance of Learning Rates in Local Update Methods
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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.
Forward citations
Cited by 4 Pith papers
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What's in a Smoothness Constant? Tighter Rates for Local SGD with Bounded Second-order Heterogeneity
Local SGD provably improves over Mini-batch SGD under bounded second-order heterogeneity in the general convex setting, with nearly tight upper and lower bounds.
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Task Arithmetic Through The Lens Of One-Shot Federated Learning
Task arithmetic is exactly one-shot FedAvg with outer step size beta = lambda T, and FedNova, FedGMA, Median, and CCLIP can often improve merged model performance.
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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization
A thesis proving communication-acceleration guarantees for local-step, compressed, Byzantine-robust, and low-rank federated optimization methods, assembled from the author's own published papers.
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What Makes Local Updates Effective: The Role of Data Heterogeneity and Smoothness
Under bounded second-order heterogeneity, local updates are shown to achieve faster convergence than mini-batch SGD in several convex and non-convex regimes, with matching lower bounds.
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