arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2602.09164cs.LG
收藏

联邦变分不等式的更快收敛速率

Faster Rates For Federated Variational Inequalities

Georgia Institute of Technology(佐治亚理工学院);Apple(苹果公司)

Guanghui Wang, Satyen Kale

AI总结:

本文提出LIPPAX算法,通过改进收敛速率和缓解客户端漂移,提升了联邦变分不等式求解的效率和性能。

摘要:

在本文中,我们研究了用于求解随机变分不等式(VIs)的联邦优化问题,这是一个近年来日益受到关注的问题。尽管已有显著进展,但现有收敛速率与联邦凸优化中已知的最先进界之间仍存在显著差距。在本文中,我们通过建立一系列改进的收敛速率来解决这一限制。首先,我们证明,对于一般的光滑且单调的变分不等式,经典的局部额外SGD算法在经过精细分析后,可以得到更紧的保证。接下来,我们识别出局部额外SGD的一个固有局限性,这可能导致客户端漂移过多。受此观察的启发,我们提出了一种新的算法,即带有额外步骤的局部不精确近似点算法(LIPPAX),并证明该算法在多个情况下可以缓解客户端漂移并实现改进的保证,包括有界Hessian、有界算子和低方差设置。最后,我们将结果扩展到联邦复合变分不等式,并建立了改进的收敛保证。

英文摘要:

In this paper, we study federated optimization for solving stochastic variational inequalities (VIs), a problem that has attracted growing attention in recent years. Despite substantial progress, a significant gap remains between existing convergence rates and the state-of-the-art bounds known for federated convex optimization. In this work, we address this limitation by establishing a series of improved convergence rates. First, we show that, for general smooth and monotone variational inequalities, the classical Local Extra SGD algorithm admits tighter guarantees under a refined analysis. Next, we identify an inherent limitation of Local Extra SGD, which can lead to excessive client drift. Motivated by this observation, we propose a new algorithm, the Local Inexact Proximal Point Algorithm with Extra Step (LIPPAX), and show that it mitigates client drift and achieves improved guarantees in several regimes, including bounded Hessian, bounded operator, and low-variance settings. Finally, we extend our results to federated composite variational inequalities and establish improved convergence guarantees.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑