Convergence of Distributed Adaptive Optimization with Local Updates
Ziheng Cheng, Margalit Glasgow
TL;DR
This paper provides the first theoretical analysis demonstrating that local adaptive optimization algorithms with intermittent communication can outperform traditional minibatch methods in certain convex settings, highlighting their communication efficiency.
Contribution
It introduces a novel contraction proof technique for local adaptive algorithms, establishing their advantages over minibatch methods in convex and weakly convex regimes.
Findings
Local SGD with momentum and Adam outperform minibatch methods in certain regimes.
The analysis relies on a new contraction technique during local iterations.
Results are applicable under generalized smoothness and gradient clipping strategies.
Abstract
We study distributed adaptive algorithms with local updates (intermittent communication). Despite the great empirical success of adaptive methods in distributed training of modern machine learning models, the theoretical benefits of local updates within adaptive methods, particularly in terms of reducing communication complexity, have not been fully understood yet. In this paper, for the first time, we prove that \em Local SGD \em with momentum (\em Local \em SGDM) and \em Local \em Adam can outperform their minibatch counterparts in convex and weakly convex settings in certain regimes, respectively. Our analysis relies on a novel technique to prove contraction during local iterations, which is a crucial yet challenging step to show the advantages of local updates, under generalized smoothness assumption and gradient clipping strategy.
Peer Reviews
Decision·ICLR 2025 Poster
The paper is a technical tour de force and the first one to analyse local methods with adaptive updates without some artificial assumption. The algorithm also incorporates the clipping mechanism to deal with the heavy-tailed noise. I think overall this is a pretty impressive display of technical achievement.
see questions.
- The work is the first to offer high-probability bounds for distributed optimization algorithms with local steps. - Some assumptions are relatively weak; for example, smoothness and (strong) convexity are required on a subset rather than the entire space. - The first theoretical convergence guarantees showing that Local SGDM and Local Adam can outperform their minibatch versions in some regimes (large $M$ and $K$ regime, where $M$ is the number of clients and $K$ is the number of local steps)
- The paper addresses only the homogeneous data case, where all clients have access to the same data. Client drift from data heterogeneity - one of the main challenges for local training methods - is not explored. - The noise assumptions are somewhat restrictive (see, e.g., [1]). Specifically, the authors assume a bounded $\alpha$-moment of the noise with $\alpha \geq 4$. In contrast, most works only assume this condition for $\alpha \in (1,2]$, and recent high-probability and in-expectation co
* This paper analyzes the convergence rates of Local SGDM and Local Adam, showing that their convergence rates are better than Minibatch SGDM and Adam. * Overall, the reviewer feels that the result shown in this paper is not very surprising, but it is solid.
* In Assumption 3, the authors assume $\alpha \geq 4$. The reviewer feels that this assumption is a bit different from the assumption commonly used in the existing literature. For instance, [1] used a similar assumption (see Assumption 1), while they called that the stochastic noise is "heavy-tailed" when $\alpha<2$. Although the authors claimed that it is easy to extend their analysis to the case where $\alpha>4$ in Remark 1, the reviewer feels that the authors should show the analysis with arb
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Taxonomy
TopicsStochastic Gradient Optimization Techniques · Advanced Bandit Algorithms Research
MethodsLocal SGD · Adam · Gradient Clipping · Stochastic Gradient Descent