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Gradient Delay Analysis in Asynchronous Distributed Optimization

Gradient-based algorithms play an important role in solving a wide range of stochastic optimization problems. In recent years, implementing such schemes in parallel has become the new paradigm. In this work, we focus on the asynchronous implementation of gradient-based algorithms. In asynchronous distributed optimization, the gradient delay problem arises since optimization parameters may be updated using stale gradients. We consider a hub-and-spoke system and derive the expected gradient staleness in terms of other system parameters such as the number of nodes, communication delay, and the expected compute time. Our derivations provide a means to compare different algorithms based on the expected gradient staleness they suffer from.