Provably accelerated decentralized gradient methods over unbalanced directed graphs

We consider the decentralized optimization problem, where a network of n agents aims to collaboratively minimize the average of their individual smooth and convex objective functions through peer -to -peer communication in a directed graph. To tackle this problem, we propose two accelerated gradient tracking methods, namely Accelerated Push-DIGing (APD) and APD-SC, for non -strongly convex and strongly convex objective functions, respectively. We show that APD \sqrt{} \mu and APD-SC converge at the rates O(k1 2 ) and O((1 - C L )k), respectively, up to constant factors depending only on the mixing matrix. APD and APD-SC are the first decentralized methods over unbalanced directed graphs that achieve the same provable acceleration as centralized methods. Numerical experiments demonstrate the effectiveness of both methods.