Before revision:  } Our stochastic gradient computation complexity is the same as the  single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
After revision:  } Our stochastic gradient computation complexity is the same as the single-machine VR methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.