Theoretical analysis and Monte Carlo simulation separate local-epoch effects from averaging and tuning effects in federated Lasso. How much local work should precede averaging when fitting a sparse regression? An orthogonal calculation shows that extra epochs can have no effect while averaging still enlarges the selected set. A correlated two-site construction gives an exact, nonmonotone limiting objective gap and its minimizing epoch count. We then compare coordinate-descent averaging, two thresholding modifications, and adapted FedDualAvg across twelve scenarios and 600 replicates. Methods share a penalty, independent validation samples, selection rules, and resource limits. FedDualAvg generally achieves smaller objective gaps but does not always recover variables better. Thresholding gains depend strongly on selection rules. Epoch effects vary with correlation, signal strength, site allocation, and the outcome measured. These results distinguish faster iteration from better optimization, prediction, and variable selection.

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