用最优传输对齐分布，让联邦学习更稳定高效
FedAVOT: Exact Distribution Alignment in Federated Learning via Masked Optimal Transport
- 将聚合过程建模为带掩码的最优传输问题
- 实现0.5精度提升，即使每轮仅2个客户端参与
- 适合数据异构、参与率低的现实场景
联邦学习（FL）可在不共享原始数据的情况下进行分布式模型训练，但当客户端参与不完全时会遭遇挑战。实践中，可用用户分布（可用性分布 $q$）与优化目标定义的分布（重要性分布 $p$）通常不一致，导致经典FedAvg出现偏差和更新不稳定。本文提出联邦平均最优传输（FedAVOT），将聚合建模为掩码最优传输问题，以对齐 $q$ 与 $p$。通过Sinkhorn缩放，FedAVOT计算基于传输的聚合权重，并具有可证明的收敛性保证。在非光滑凸联邦学习设定下，达到标准 $/mathcal{O}(1/ ext{√}T)$ 收敛速率，且不依赖每轮参与客户端数量。实验表明，相较于FedAvg，FedAVOT在异构、公平敏感及低可用性场景下性能显著提升，即使每轮仅有两个客户端参与。
原文摘要 · Abstract (English)
Federated Learning (FL) allows distributed model training without sharing raw data, but suffers when client participation is partial. In practice, the distribution of available users (\emph{availability distribution} $q$) rarely aligns with the distribution defining the optimization objective (\emph{importance distribution} $p$), leading to biased and unstable updates under classical FedAvg. We propose \textbf{Fereated AVerage with Optimal Transport (\textbf{FedAVOT})}, which formulates aggregation as a masked optimal transport problem aligning $q$ and $p$. Using Sinkhorn scaling, \textbf{FedAVOT} computes transport-based aggregation weights with provable convergence guarantees. \textbf{FedAVOT} achieves a standard $\mathcal{O}(1/\sqrt{T})$ rate under a nonsmooth convex FL setting, independent of the number of participating users per round. Our experiments confirm drastically improved performance compared to FedAvg across heterogeneous, fairness-sensitive, and low-availability regimes, even when only two clients participate per round.
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