  Parallelism is a ubiquitous method for accelerating machine learning
algorithms. However, theoretical analysis of parallel learning is usually done
in an algorithm- and protocol-specific setting, giving little insight about how
changes in the structure of communication could affect convergence. In this
paper we propose MixML, a general framework for analyzing convergence of weakly
consistent parallel machine learning. Our framework includes: (1) a unified way
of modeling the communication process among parallel workers; (2) a new
parameter, the mixing time tmix, that quantifies how the communication process
affects convergence; and (3) a principled way of converting a convergence proof
for a sequential algorithm into one for a parallel version that depends only on
tmix. We show MixML recovers and improves on known convergence bounds for
asynchronous and/or decentralized versions of many algorithms, includingSGD and
AMSGrad. Our experiments substantiate the theory and show the dependency of
convergence on the underlying mixing time.
