Scaffold with Stochastic Gradients: New Analysis with Linear Speed-Up

• URL: http://arxiv.org/abs/2503.07594v1
• Date: Mon, 10 Mar 2025 17:56:19 GMT
• Title: Scaffold with Stochastic Gradients: New Analysis with Linear Speed-Up
• Authors: Paul Mangold, Alain Durmus, Aymeric Dieuleveut, Eric Moulines,
• Abstract summary: We show that Scaffold achieves linear speed-up in the number of clients up to higher-order terms in the step size.<n>Our analysis reveals that Scaffold retains a higher-order bias, similar to FedAvg, that does not decrease as the number of clients increases.
• Score: 29.55535031689754
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes a novel analysis for the Scaffold algorithm, a popular method for dealing with data heterogeneity in federated learning. While its convergence in deterministic settings--where local control variates mitigate client drift--is well established, the impact of stochastic gradient updates on its performance is less understood. To address this problem, we first show that its global parameters and control variates define a Markov chain that converges to a stationary distribution in the Wasserstein distance. Leveraging this result, we prove that Scaffold achieves linear speed-up in the number of clients up to higher-order terms in the step size. Nevertheless, our analysis reveals that Scaffold retains a higher-order bias, similar to FedAvg, that does not decrease as the number of clients increases. This highlights opportunities for developing improved stochastic federated learning algorithms

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