用几何轨迹优化异步联邦学习，提升准确率与公平性
Aggregation on Learnable Manifolds for Asynchronous Federated Optimization
- 将参数聚合建模为流形上的曲线学习，避免损失障碍
- 在三个数据集上准确率优于主流异步方法，公平性显著提升
- 适合异构设备、高延迟场景下的联邦学习应用
异步联邦学习中，异构客户端面临两大挑战：标准线性插值（如FedAvg）易受曲率影响产生损失屏障，以及过时更新与服务器状态错位引发干扰。为此，我们提出一个几何框架，将聚合视为黎曼模型空间中的曲线学习，并解耦轨迹选择与更新冲突处理。在此框架下，提出AsyncBezier，以低阶多项式（贝塞尔）轨迹替代线性聚合，绕过损失屏障；提出OrthoDC，通过基于内积的正交投影对延迟更新进行修正，降低干扰。在一般任务与医疗领域三组数据集（包括LEAF Shakespeare和FEMNIST）上，该方法持续提升准确率与客户端公平性，优于强基线；且即使其他方法拥有更高本地计算预算，其性能优势仍保持不变。
原文摘要 · Abstract (English)
Asynchronous federated learning (FL) with heterogeneous clients faces two key issues: curvature-induced loss barriers encountered by standard linear parameter interpolation techniques (e.g. FedAvg) and interference from stale updates misaligned with the server's current optimisation state. To alleviate these issues, we introduce a geometric framework that casts aggregation as curve learning in a Riemannian model space and decouples trajectory selection from update conflict resolution. Within this, we propose AsyncBezier, which replaces linear aggregation with low-degree polynomial (Bezier) trajectories to bypass loss barriers, and OrthoDC, which projects delayed updates via inner product-based orthogonality to reduce interference. We establish framework-level convergence guarantees covering each variant given simple assumptions on their components. On three datasets spanning general-purpose and healthcare domains, including LEAF Shakespeare and FEMNIST, our approach consistently improves accuracy and client fairness over strong asynchronous baselines; finally, we show that these gains are preserved even when other methods are allocated a higher local compute budget.
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