改进联邦学习算法，让计算不精确时仍能稳定收敛。
On the Convergence of FedProx with Extrapolation and Inexact Prox
- 引入服务器端外推与不精确近端更新，放宽理想假设。
- 证明不精确性导致收敛到解的邻域，但可控制影响。
- 分析本地优化器迭代次数对精度的影响，适合实际部署者参考。
在平滑且全局强凸条件下，本文研究了无精确近端计算假设下的FedExProx算法行为。理论表明，不精确性会导致算法收敛至解的邻域，但通过合理调控，其负面影响可被缓解。我们进一步将不精确性与有偏压缩（biased compression）关联，揭示外推机制对近端更新不精确的鲁棒性。同时，分析了不同本地优化器实现所需局部迭代次数以达到指定不精确度。理论结果通过全面数值实验验证。
原文摘要 · Abstract (English)
Enhancing the FedProx federated learning algorithm (Li et al., 2020) with server-side extrapolation, Li et al. (2024a) recently introduced the FedExProx method. Their theoretical analysis, however, relies on the assumption that each client computes a certain proximal operator exactly, which is impractical since this is virtually never possible to do in real settings. In this paper, we investigate the behavior of FedExProx without this exactness assumption in the smooth and globally strongly convex setting. We establish a general convergence result, showing that inexactness leads to convergence to a neighborhood of the solution. Additionally, we demonstrate that, with careful control, the adverse effects of this inexactness can be mitigated. By linking inexactness to biased compression (Beznosikov et al., 2023), we refine our analysis, highlighting robustness of extrapolation to inexact proximal updates. We also examine the local iteration complexity required by each client to achieved the required level of inexactness using various local optimizers. Our theoretical insights are validated through comprehensive numerical experiments.
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