Age-Based Coded Computation for Bias Reduction in Distributed Learning

Coded computation can speed up distributed learning in the presence of straggling workers. Partial recovery of the gradient vector can further reduce the computation time at each iteration; however, this can result in biased estimators, which may slow down convergence, or even cause divergence. Estimator bias is particularly prevalent when the straggling behavior is correlated over time, which results in the gradient estimators being dominated by a few fast servers. To mitigate biased estimators, we design a timely dynamic encoding framework for partial recovery that includes an ordering operator that changes the codewords and computation orders at workers over time. To regulate the recovery frequencies, we adopt an age metric in the design of the dynamic encoding scheme. The proposed age-based scheme prioritizes the recovery of computations with relatively large age. We show through numerical results that the proposed dynamic encoding strategy increases the timeliness of the recovered computations, which, as a result, reduces the bias in model updates, and accelerates the convergence compared to conventional static partial recovery schemes.