标题： 改进的联邦平均偏差分析与联邦Richardson-Romberg外推法 显示英文标题

标题： Refined Analysis of Federated Averaging's Bias and Federated Richardson-Romberg Extrapolation

摘要： 本文中，我们提出了FedAvg算法在常数步长下的新颖分析，依赖于底层过程的马尔可夫性质。 我们证明了算法的全局迭代收敛到一个平稳分布，并分析了相对于问题解的结果偏差和方差。 我们在同质和异质设定下提供了偏差的一阶展开。 有趣的是，这个偏差分解为两个不同的部分：一个仅依赖于随机梯度噪声，另一个依赖于客户端异质性。 最后，我们基于理查森-罗姆伯格外推技术引入了一种新算法以减轻这种偏差。 显示英文摘要

摘要： In this paper, we present a novel analysis of FedAvg with constant step size, relying on the Markov property of the underlying process. We demonstrate that the global iterates of the algorithm converge to a stationary distribution and analyze its resulting bias and variance relative to the problem's solution. We provide a first-order expansion of the bias in both homogeneous and heterogeneous settings. Interestingly, this bias decomposes into two distinct components: one that depends solely on stochastic gradient noise and another on client heterogeneity. Finally, we introduce a new algorithm based on the Richardson-Romberg extrapolation technique to mitigate this bias.