重新分析联邦优化方法FedExProx，证明其在特定条件下比普通梯度下降更快收敛。
Tighter Performance Theory of FedExProx
- 构建新理论框架，更精准刻画非强凸二次问题的收敛速度。
- 考虑计算与通信开销，证明FedExProx可严格优于梯度下降。
- 适用于弱凸函数和部分参与场景，对联邦学习具启发意义。
我们重新审视了近期提出的分布式优化方法FedExProx，该方法通过外推提升并行近端算法的收敛性。研究发现，其在二次优化任务上的理论保证并不优于基础梯度下降（GD）方法。基于此，我们提出新的分析框架，为非强凸二次问题建立了更紧的线性收敛速率。在同时考虑计算与通信成本的前提下，证明FedExProx可严格优于GD，与原分析结论形成鲜明对比。进一步研究部分参与场景，分析了基于梯度多样性与Polyak步长的两种自适应外推策略，性能显著超越先前结果。此外，将分析拓展至满足Polyak-Lojasiewicz条件的一般函数，相较于以往强凸假设下的分析更具优势，且条件更弱。实验验证支持上述结论，表明FedExProx具有更强潜力，为外推技术在联邦学习中的应用开辟新路径。
原文摘要 · Abstract (English)
We revisit FedExProx - a recently proposed distributed optimization method designed to enhance convergence properties of parallel proximal algorithms via extrapolation. In the process, we uncover a surprising flaw: its known theoretical guarantees on quadratic optimization tasks are no better than those offered by the vanilla Gradient Descent (GD) method. Motivated by this observation, we develop a novel analysis framework, establishing a tighter linear convergence rate for non-strongly convex quadratic problems. By incorporating both computation and communication costs, we demonstrate that FedExProx can indeed provably outperform GD, in stark contrast to the original analysis. Furthermore, we consider partial participation scenarios and analyze two adaptive extrapolation strategies - based on gradient diversity and Polyak stepsizes - again significantly outperforming previous results. Moving beyond quadratics, we extend the applicability of our analysis to general functions satisfying the Polyak-Lojasiewicz condition, outperforming the previous strongly convex analysis while operating under weaker assumptions. Backed by empirical results, our findings point to a new and stronger potential of FedExProx, paving the way for further exploration of the benefits of extrapolation in federated learning.
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