Stabilized Proximal-Point Methods for Federated Optimization

• URL: http://arxiv.org/abs/2407.07084v2
• Date: Sun, 3 Nov 2024 10:13:18 GMT
• Title: Stabilized Proximal-Point Methods for Federated Optimization
• Authors: Xiaowen Jiang, Anton Rodomanov, Sebastian U. Stich,
• Abstract summary: Best-known communication complexity among non-accelerated algorithms is achieved by DANE, a distributed proximal-point algorithm. Inspired by the hybrid-projection proximal-point method, we propose a novel distributed algorithm S-DANE. We show that S-DANE achieves the best-known communication complexity while still enjoying good local computation efficiency as S-DANE.
• Score: 20.30761752651984
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In developing efficient optimization algorithms, it is crucial to account for communication constraints -- a significant challenge in modern Federated Learning. The best-known communication complexity among non-accelerated algorithms is achieved by DANE, a distributed proximal-point algorithm that solves local subproblems at each iteration and that can exploit second-order similarity among individual functions. However, to achieve such communication efficiency, the algorithm requires solving local subproblems sufficiently accurately resulting in slightly sub-optimal local complexity. Inspired by the hybrid-projection proximal-point method, in this work, we propose a novel distributed algorithm S-DANE. Compared to DANE, this method uses an auxiliary sequence of prox-centers while maintaining the same deterministic communication complexity. Moreover, the accuracy condition for solving the subproblem is milder, leading to enhanced local computation efficiency. Furthermore, S-DANE supports partial client participation and arbitrary stochastic local solvers, making it attractive in practice. We further accelerate S-DANE and show that the resulting algorithm achieves the best-known communication complexity among all existing methods for distributed convex optimization while still enjoying good local computation efficiency as S-DANE. Finally, we propose adaptive variants of both methods using line search, obtaining the first provably efficient adaptive algorithms that could exploit local second-order similarity without the prior knowledge of any parameters.

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