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Refined Analysis of Constant Step Size Federated Averaging and . . . In this paper, we present a novel analysis of $\texttt {FedAvg}$ 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 bias expansion in both homogeneous and