Private Stochastic Convex Optimization: Efficient Algorithms for Non-smooth Objectives

In this paper, we revisit the problem of private stochastic convex optimization. We propose an algorithm, based on noisy mirror descent, which achieves optimal rates up to a logarithmic factor, both in terms of statistical complexity and number of queries to a first-order stochastic oracle. Unlike prior work, we do not require Lipschitz continuity of stochastic gradients to achieve optimal rates. Our algorithm generalizes beyond the Euclidean setting and yields anytime utility and privacy guarantees.