ELNUR GASANOV

We propose and study a new class of gradient communication mechanisms for communication-efficient training-three point compressors (3PC)-as well as efficient distributed nonconvex optimization algorithms that can take advantage of them. Unlike most established approaches, which rely on a static compressor choice (e.g., Top- ), our class allows the compressors to evolve throughout the training process, with the aim of improving the theoretical communication complexity and practical efficiency of the underlying methods. We show that our general approach can recover the recently proposed state-of-the-art error feedback mechanism EF21 (Richtarik et al., 2021) and its theoretical properties as a special case, but also leads to a number of new efficient methods. Notably, our approach allows us to improve upon the state-of-the-art in the algorithmic and theoretical foundations of the lazy aggregation literature (Chen et al., 2018). As a by-product that may be of independent interest, we..