Is Local SGD Better than Minibatch SGD? (2002.07839v2)

Abstract: We study local SGD (also known as parallel SGD and federated averaging), a natural and frequently used stochastic distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minimax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least sometimes improves over minibatch SGD; (3) We show that indeed local SGD does not dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.

• The paper shows that local SGD achieves minimax optimality for quadratic objectives through accelerated methods.
• It reveals that for general convex objectives, local SGD can outperform minibatch SGD under large worker counts and frequent local updates.
• The study derives performance bounds, highlighting regimes where local SGD may excel or lag, thus guiding method selection in distributed optimization.

Is Local SGD Better than Minibatch SGD? An Analytical Perspective

The research paper "Is Local SGD Better than Minibatch SGD?" offers a theoretical examination of local stochastic gradient descent (SGD) in comparison to the more traditional minibatch SGD. The method of local SGD, which is also known as parallel SGD or federated averaging, has gained popularity in the domain of distributed optimization of large-scale convex and non-convex problems, including federated learning scenarios. Despite its widespread use, the theoretical foundations of local SGD remain insufficiently developed, making this comparative analysis critical for understanding its true efficacy.

Core Contributions and Findings

The paper primarily investigates whether local SGD can outperform minibatch SGD in various settings. The authors present a nuanced argument that challenges the commonly held belief that local SGD is superior by default. Here are the core findings:

1. Quadratic Objectives: The paper successfully demonstrates that local SGD provides a strict improvement over minibatch SGD for quadratic objectives. It is shown through rigorous proofs that accelerated local SGD approaches can achieve minimax optimality, presenting a compelling case that local SGD is theoretically favored in the quadratic setting.
2. General Convex Objectives: For general convex objectives, this work presents the first error guarantee indicating that local SGD can sometimes surpass minibatch SGD, specifically under parameters where the number of workers is large and the number of local updates per round is substantial. However, they also establish that local SGD's performance is not universally better, as there exists a lower bound on its performance where local SGD can be worse than minibatch SGD.
3. Performance Bounds: The authors derive a range of performance bounds for local SGD, offering a sophisticated analysis that takes into account issues like the variance of the gradients and convergence rates. These bounds importantly show regimes where local SGD could outperform, match, or be outperformed by minibatch SGD—highlighting the complexity and dependency of the performance on the specific optimization landscape.

Theoretical and Practical Implications

The implications of this research are substantial. Practically, it enlightens practitioners on the conditions under which local SGD should be preferred or avoided. Theoretically, it enhances our understanding of distributed optimization methods, bridging a gap in literature regarding the comparison of local SGD with minibatch SGD.

Moreover, this paper identifies circumstances where local SGD may not perform optimally and suggests avenues for future algorithmic developments. In light of these findings, the paper discourages blanket assumptions about local SGD's superiority and instead recommends algorithmic consideration be based on the specific properties of the optimization problem at hand.

Future Directions

Continued research could focus on developing new algorithms that combine the advantages of both local SGD and minibatch SGD. Moreover, tightening the bounds for local SGD and further exploring the non-quadratic scenario dynamics contribute vital paths for further paper. Expanding upon the local SGD approach could also offer more nuanced mechanisms that retain performance benefits across a broader spectrum of problems.

In summary, "Is Local SGD Better than Minibatch SGD?" provides a meticulous analysis that advances the theoretical understanding of local SGD, highlighting its potential advantages and limitations in a structured and computationally varied landscape. The paper suggests that there is no one-size-fits-all in distributed optimization, reinforcing that algorithm selection should be heavily dictated by problem-specific characteristics and computational environments.