This paper investigates the convergence of unadjusted Langevin algorithm (ULA) under the log-Sobolev inequality condition and shows convergence with respect to Reny divergence, which generalizes the existing results for KL-divergence. The analysis for the convergence on the Reny divergence is novel and interesting. However, Theorems 1 and 2 require some more discussions about comparison with existing studies. Actually, reviewer 3 pointed out the following paper: [3] Ma, Yi-An, et al. "Is There an Analog of Nesterov Acceleration for MCMC?." arXiv preprint arXiv:1902.00996 This paper shows the exponential convergence under the log-Sobolev inequality in its Sec.