Provable Reduction in Communication Rounds for Non-Smooth Convex Federated Learning

Multiple local steps are key to communication-efficient federated learning. However, theoretical guarantees for such algorithms, without data heterogeneity-bounding assumptions, have been lacking in general non-smooth convex problems. Leveraging projection-efficient optimization methods, we propose FedMLS, a federated learning algorithm with provable improvements from multiple local steps. FedMLS attains an $\epsilon$-suboptimal solution in $\mathcal{O}(1\mathrm{/}\epsilon )$ communication rounds, requiring a total of $\mathcal{O}(1\mathrm{/}{\epsilon }^2)$ stochastic subgradient oracle calls.