Local SGD Converges Fast and Communicates Little (1805.09767v3)

Abstract: Mini-batch stochastic gradient descent (SGD) is state of the art in large scale distributed training. The scheme can reach a linear speedup with respect to the number of workers, but this is rarely seen in practice as the scheme often suffers from large network delays and bandwidth limits. To overcome this communication bottleneck recent works propose to reduce the communication frequency. An algorithm of this type is local SGD that runs SGD independently in parallel on different workers and averages the sequences only once in a while. This scheme shows promising results in practice, but eluded thorough theoretical analysis. We prove concise convergence rates for local SGD on convex problems and show that it converges at the same rate as mini-batch SGD in terms of number of evaluated gradients, that is, the scheme achieves linear speedup in the number of workers and mini-batch size. The number of communication rounds can be reduced up to a factor of T^{1/2}---where T denotes the number of total steps---compared to mini-batch SGD. This also holds for asynchronous implementations. Local SGD can also be used for large scale training of deep learning models. The results shown here aim serving as a guideline to further explore the theoretical and practical aspects of local SGD in these applications.

Local SGD Converges Fast and Communicates Little

The paper "Local SGD Converges Fast and Communicates Little" by Sebastian U. Stich presents an in-depth theoretical and empirical analysis of Local Stochastic Gradient Descent (Local SGD), addressing both its convergence properties and communication efficiency in distributed machine learning settings. This work offers significant insights into optimization algorithms, particularly for training large-scale machine learning models with distributed computational resources.

Overview

The motivation for this research arises from the need to mitigate the communication bottlenecks in distributed training using Mini-batch Stochastic Gradient Descent (SGD). Traditional parallel mini-batch SGD, while theoretically promising linear speedup, often suffers in practice due to high communication overheads between the worker nodes. Local SGD proposes a strategy where multiple worker nodes perform SGD independently for several iterations before synchronizing the model parameters, thus reducing the frequency of communication.

Main Contributions

1. Theoretical Convergence Analysis: The paper provides rigorous theoretical guarantees for Local SGD on convex optimization problems. It establishes that Local SGD converges at the same rate as mini-batch SGD concerning the number of gradient evaluations. Furthermore, it shows that the number of communication rounds required can be decreased by a factor of $T^{1/2}$, where $T$ is the total number of iterations.
2. Asynchronous Local SGD: The research extends the analysis to asynchronous Local SGD, where worker nodes do not need to synchronize precisely at the same iterations. This analysis is particularly useful for heterogeneous environments where different workers may have varying computation speeds.
3. Empirical Validation: The paper also includes numerical experiments illustrating the speedup achieved by Local SGD under practical settings, confirming the theoretical findings. These experiments highlight the potential benefits of reduced communication overheads and improved scalability of Local SGD in distributed machine learning tasks.

Theoretical Results

The primary theoretical results can be summarized as follows:

• Local SGD achieves an $\mathcal{O}(\frac{1}{K T})$ convergence rate for convex optimization problems with $K$ workers and a mini-batch size of $b$.
• The scheme can reduce the communication rounds by up to a factor of $T^{1/2}$ compared to mini-batch SGD without degrading the convergence rate.
• For asynchronous implementations, Local SGD can tolerate delays up to $O(\sqrt{T/K})$, maintaining the same asymptotic convergence rate as synchronous Local SGD.

Discussion

Practical Implications

The practical implications of these theoretical findings are significant:

• Reduced Communication Overheads: In large-scale machine learning, communication between worker nodes is a major bottleneck. Local SGD's ability to reduce the number of synchronization points directly addresses this issue, making it highly effective for training deep neural networks and other large models.
• Scalability: The linear speedup in terms of the number of workers and mini-batch size enables efficient scaling of machine learning training processes across multiple computing nodes.
• Asynchronous Execution: The resilience to delays in asynchronous execution makes Local SGD suitable for heterogeneous environments, where computational resources may vary in performance.

Future Directions

This work opens several avenues for future research:

• Non-Convex Optimization: Extending the theoretical analysis to non-convex problems, which are prevalent in deep learning, remains an open challenge. Initial empirical evidence suggests potential benefits in this domain.
• Adaptive Synchronization: Developing adaptive strategies for determining synchronization intervals dynamically based on the progress of the optimization process can further enhance the efficiency of Local SGD.
• Combined Approaches: Investigating Local SGD in combination with other techniques, such as gradient sparsification and quantization, could lead to even greater reductions in communication overheads.

Conclusion

The paper "Local SGD Converges Fast and Communicates Little" provides a comprehensive theoretical and empirical analysis of Local SGD, demonstrating its potential to achieve fast convergence with minimal communication. This work is valuable for advancing distributed optimization algorithms, particularly in the context of large-scale machine learning. The findings have significant implications for both the theoretical understanding and practical deployment of distributed training frameworks, offering a robust solution to one of the critical challenges in the field.