iFedDR: Auto-Tuning Local Computation with Inexact Douglas-Rachford Splitting in Federated Learning

Thomas Pethick, Puya Latafat, Basile Lewandowski, Zheng Xu, Peter Kairouz, Panagiotis Patrinos, Volkan Cevher

Keywords: Federated learning, Douglas-Rachford splitting, monotone operators, relative error, inexact proximal point

TL;DR: We introduce an error-corrected version of FedDR that mitigates the need to predefine the number of client steps

Abstract: Federated learning usually requires specifying the amount of local computation needed a priori. In this work, we instead propose a systematic scheme to automatically adjust and potentially reduce the local computations while preserving convergence guarantees. We focus on proximal-based methods, where we demonstrate that the proximal operator can be evaluated inexactly up to a relative error, rather than relying on a predefined sequence of vanishing errors. Our proposed method, iFedDR, is based on a novel error-corrected version of inexact Douglas-Rachford splitting. It mitigates the need for hyperparameter tuning the number of client steps, by triggering refinement on-demand. We derive iFedDR as an instance of a much more general construction, which allows us to handle minimax problem, and which is interesting in its own right. Several numerical experiments are carried out demonstrating the favorable convergence properties of iFedDR.

Primary Area: optimization

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Submission Number: 10234