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In Proceedings of Uncertainty in Artificial Intelligence, 31-4 August 2023, Pittsburgh, PA, USA While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains a challenge. We study nonconvex ERM, which takes the form of minimizing a finite-sum of nonconvex loss functions over a training set. We propose a new differentially private stochastic gradient descent algorithm for nonconvex ERM that achieves strong privacy guarantees efficiently, and provide a tight analysis of its privacy and utility guarantees, as well as its gradient complexity. Our algorithm reduces gradient complexity while matching the best-known utility guarantee. Our experiments on benchmark nonconvex ERM problems demonstrate superior performance in terms of both training cost and utility gains compared with previous differentially private methods using the same privacy budgets. 

Property inference attacks reveal statistical properties about a training set but are difficult to distinguish from the primary purposes of statistical machine learning, which is to produce models that capture statistical properties about a distribution. Motivated by Yeom et al.’s membership inference framework, we propose a formal and generic definition of property inference attacks. The proposed notion describes attacks that can distinguish between possible training distributions, extending beyond previous property inference attacks that infer the ratio of a particular type of data in the training data set. In this paper, we show how our definition captures previous property inference attacks as well as a new attack that reveals the average degree of nodes of a training graph and report on experiments giving insight into the potential risks of property inference attacks.