  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 APD and APD-SC, for non-strongly convex and strongly convex
objective functions, respectively. We show that APD and APD-SC converge at the
rates $O\left(\frac{1}{k^2}\right)$ and $O\left(\left(1 -
C\sqrt{\frac{\mu}{L}}\right)^k\right)$, 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.
