Title: Optimal Membership Inference Bounds for Adaptive Composition of Sampled Gaussian Mechanisms. Abstract: Given a trained model and a data sample, membership-inference (MI) attacks predict whether the sample was in the model’s training set. A common counter- measure against MI attacks is to utilize differential privacy (DP) during model training to mask the presence of individual examples. While this use of DP is a principled approach to limit the efficacy of MI attacks, there is a gap between the bounds provided by DP and the empirical performance of MI attacks. In this paper, we derive bounds for the advantage of an adversary mounting a MI attack, and demonstrate tightness for the widely-used Gaussian mechanism. Our analysis answers an open problem in the field of differential privacy, namely the fact that membership inference is not 100% successful even for relatively high budgets ($\epsilon> 10$). Finally, using our analysis, we provide MI metrics for models trained on CIFAR10 dataset. To the best of our knowledge, our analysis provides the state-of-the-art membership inference bounds.