Local Steps Speed Up Local GD for Heterogeneous Distributed Logistic Regression

Michael Crawshaw, Blake Woodworth, Mingrui Liu

Keywords: optimization, convex optimization, distributed optimization, federated learning, logistic regression

TL;DR: This paper provides an improved analysis for local gd which proves the benefit of local steps for heterogeneous logistic regression.

Abstract:

We analyze two variants of Local Gradient Descent applied to distributed logistic regression with heterogeneous, separable data and show convergence at the rate $O(1/KR)$ for $K$ local steps and sufficiently large $R$ communication rounds. In contrast, all existing convergence guarantees for Local GD applied to any problem are at least $\Omega(1/R)$, meaning they fail to show the benefit of local updates. The key to our improved guarantee is showing progress on the logistic regression objective when using a large stepsize $\eta \gg 1/K$, whereas prior analysis depends on $\eta \leq 1/K$.

Primary Area: optimization

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Submission Number: 10896