Accelerating Optimization and Machine Learning through Decentralization

Decentralized optimization enables multiple devices to learn a global machine learning model while each individual device only has access to its local dataset. By avoiding the need for training data to leave individual users' devices, it enhances privacy and scalability compared to conventional centralized learning, where all data has to be aggregated to a central server. However, decentralized optimization has traditionally been viewed as a necessary compromise, used only when centralized processing is impractical due to communication constraints or data privacy concerns. In this study, we show that decentralization can paradoxically accelerate convergence, outperforming centralized methods in the number of iterations needed to reach optimal solutions. Through examples in logistic regression and neural network training, we demonstrate that distributing data and computation across multiple agents can lead to faster learning than centralized approaches, even when each iteration is assumed to take the same amount of time, whether performed centrally on the full dataset or decentrally on local subsets. This finding challenges longstanding assumptions and reveals decentralization as a strategic advantage, offering new opportunities for more efficient optimization and machine learning.

Provable Acceleration of Distributed Optimization with Local Updates

In conventional distributed optimization, each agent performs a single local update between two communication rounds with its neighbors to synchronize solutions. Inspired by the success of using multiple local updates in federated learning, incorporating local updates into distributed optimization has recently attracted increasing attention. However, unlike federated learning, where multiple local updates can accelerate learning by improving gradient estimation under mini-batch settings, it remains unclear whether similar benefits hold in distributed optimization when gradients are exact. Moreover, existing theoretical results typically require reducing the step size when multiple local updates are employed, which can entirely offset any potential benefit of these additional local updates and obscure their true impact on convergence. In this paper, we focus on the classic DIGing algorithm and leverage the tight performance bounds provided by Performance Estimation Problems (PEP) to show that incorporating local updates can indeed accelerate distributed optimization. To the best of our knowledge, this is the first rigorous demonstration of such acceleration for a broad class of objective functions. Our analysis further reveals that, under an appropriate step size, performing only two local updates is sufficient to achieve the maximal possible improvement, and that additional local updates provide no further gains. Because more updates increase computational cost, these findings offer practical guidance for efficient implementation. Extensive experiments on both synthetic and real-world datasets corroborate the theoretical findings.