  In the setting of federated optimization, where a global model is aggregated
periodically, step asynchronism occurs when participants conduct model training
by efficiently utilizing their computational resources. It is well acknowledged
that step asynchronism leads to objective inconsistency under non-i.i.d. data,
which degrades the model's accuracy. To address this issue, we propose a new
algorithm FedaGrac, which calibrates the local direction to a predictive global
orientation. Taking advantage of the estimated orientation, we guarantee that
the aggregated model does not excessively deviate from the global optimum while
fully utilizing the local updates of faster nodes. We theoretically prove that
FedaGrac holds an improved order of convergence rate than the state-of-the-art
approaches and eliminates the negative effect of step asynchronism. Empirical
results show that our algorithm accelerates the training and enhances the final
accuracy.
