Review for NeurIPS paper: Faster Differentially Private Samplers via Rényi Divergence Analysis of Discretized Langevin MCMC

Despite hinting at such a result multiple times in the paper, the results presented in this paper does not directly imply pure or approximate differential privacy for an algorithm that runs Langevin dynamics for T-iterations. At least it is not a trivial argument that goes through without further assumptions. The reason is the following: The Renyi Divergence bound on D(P R) (the order \alpha is abbreviated for readability) does not seem to imply a differential privacy bound overall, even though a sample from R satisfies DP. The DP bound of posterior sampling implies a bound on D(R R'). By results of this paper, we have bounds on D(P R) and D(P' R').