“…In terms of communication cost, there is a large body of work developing communication efficient algorithms by either reducing communication frequency [9,10,11,12,13] or reducing message size [14,15,16,17,18] by employing techniques like quantization and sparsification. See [19] and [20] for a detailed survey of such approaches. However, as mentioned earlier, most of these works treat the two components of communication cost separately and hence focus on reducing only one of these two components.…”