Adaptive Diffusion With Compressed Communication

We consider multi-agent networks that aim at solving, cooperatively and online, distributed optimization problems under communication constraints. We propose the ACTC (Adapt-Compress-Then-Combine) diffusion strategy, which leverages differential randomized compression to infuse the classical ATC strategy with the ability to handle compressed data. We consider the flexible setting of directed graphs and left-stochastic policies, and require strong convexity only at a network level (i.e., some agents might even have non-convex risks). We prove that each agent is able to learn the optimal solution up to a small error on the order of the step-size, achieving remarkable savings in terms of bits exchanged between neighboring agents.