  Analysis of the convergence rates of modern convex optimization algorithms
can be achived through binary means: analysis of emperical convergence, or
analysis of theoretical convergence. These two pathways of capturing
information diverge in efficacy when moving to the world of distributed
computing, due to the introduction of non-intuitive, non-linear slowdowns
associated with broadcasting, and in some cases, gathering operations. Despite
these nuances in the rates of convergence, we can still show the existence of
convergence, and lower bounds for the rates. This paper will serve as a helpful
cheat-sheet for machine learning practitioners encountering this problem class
in the field.
