Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronization (1910.13598v2)

Abstract: Communication overhead is one of the key challenges that hinders the scalability of distributed optimization algorithms. In this paper, we study local distributed SGD, where data is partitioned among computation nodes, and the computation nodes perform local updates with periodically exchanging the model among the workers to perform averaging. While local SGD is empirically shown to provide promising results, a theoretical understanding of its performance remains open. We strengthen convergence analysis for local SGD, and show that local SGD can be far less expensive and applied far more generally than current theory suggests. Specifically, we show that for loss functions that satisfy the Polyak-{\L}ojasiewicz condition, $O((pT)^{1/3})$ rounds of communication suffice to achieve a linear speed up, that is, an error of $O(1/pT)$, where $T$ is the total number of model updates at each worker. This is in contrast with previous work which required higher number of communication rounds, as well as was limited to strongly convex loss functions, for a similar asymptotic performance. We also develop an adaptive synchronization scheme that provides a general condition for linear speed up. Finally, we validate the theory with experimental results, running over AWS EC2 clouds and an internal GPU cluster.

Insights into Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronization

The paper entitled "Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronization," authored by Haddadpour et al., addresses one of the pressing challenges in distributed optimization, namely the communication overhead. The focus is on local Stochastic Gradient Descent (SGD), where the exchange of information between nodes is minimized through periodic averaging of local updates.

Summary and Key Results

The authors introduce a refined convergence analysis for local SGD, demonstrating that it can achieve linear speedup under more general conditions than previously established in the literature. The key findings can be summarized as follows:

1. Reduced Communication Rounds: The paper shows that for loss functions satisfying the Polyak-Lojasiewicz (PL) condition, it is sufficient to perform $O((pT)^{1/3})$ communication rounds to achieve linear convergence speed up, obtaining an error rate of $O(1/pT)$. This is a significant improvement from previous works which required $O(\sqrt{pT})$ communication rounds under stronger assumptions such as strong convexity.
2. Adaptive Synchronization Scheme: Beyond the fixed periodic averaging, the paper introduces an adaptive synchronization scheme that further reduces communication overhead by adjusting the frequency of averaging dynamically based on the state of the optimization.
3. Experimental Validation: The theoretical results are validated with experiments conducted on both an AWS EC2 cloud setup and an internal GPU cluster, demonstrating practical reductions in communication costs while maintaining convergence speed.

Methodological Contributions

The authors leverage the PL condition, which extends the applicability beyond strongly convex functions, to prove tighter bounds on the convergence of local SGD. The analytical approach focuses on bounding the variance reduction through averaging, thus enabling fewer synchronization points while preserving convergence rates.

Implications and Future Directions

The implications of this paper are twofold. Practically, the reduced need for communication in a distributed setting implies potential savings in network resources and increased scalability for training large-scale models, particularly in deep learning contexts. Theoretically, this work opens avenues for further exploration of communication-efficient algorithms under broader classes of functions, including non-convex landscapes routinely encountered in machine learning.

Future directions could include investigating the lower bounds of communication-computation tradeoffs in distributed SGD, exploring the potential for even larger intervals of local updates, and examining the interplay between communication costs and other distributed computing factors such as fault tolerance and straggler effects.

The rigorous analysis and experiments presented signify an important step towards efficient distributed optimization in the era of big data and deep models, driving advancements in areas requiring distributed computation across varied computing environments.