Faster Differentially Private Samplers via Rényi Divergence Analysis of Discretized Langevin MCMC
AuthorsArun Ganesh, Kunal Talwar
Various differentially private algorithms instantiate the exponential mechanism, and require sampling from the distribution exp(−f) for a suitable function f. When the domain of the distribution is high-dimensional, this sampling can be computationally challenging. Using heuristic sampling schemes such as Gibbs sampling does not necessarily lead to provable privacy. When f is convex, techniques from log-concave sampling lead to polynomial-time algorithms, albeit with large polynomials. Langevin dynamics-based algorithms offer much faster alternatives under some distance measures such as statistical distance. In this work, we establish rapid convergence for these algorithms under distance measures more suitable for differential privacy. For smooth, strongly-convex f, we give the first results proving convergence in Rényi divergence. This gives us fast differentially private algorithms for such f. Our techniques and simple and generic and apply also to underdamped Langevin dynamics.
Earlier this year, Apple hosted the Privacy-Preserving Machine Learning (PPML) workshop. This virtual event brought Apple and members of the academic research communities together to discuss the state of the art in the field of privacy-preserving machine learning through a series of talks and discussions over two days.