Abstract We consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Most prior works on differentially private stochastic convex optimization for heavy-tailed data are either restricted to gradient descent (GD) or performed multi-times clipping on stochastic gradient descent (SGD), which is inefficient for large-scale problems. In this paper, we consider a one-time clipping strategy and provide principled analyses of its bias and private mean estimation. We establish new convergence results and improved complexity bounds for the proposed algorithm called AClipped-dpSGD for constrained and unconstrained convex problems. We also extend our convergent analysis to the strongly convex case and non-smooth case (which works for generalized smooth objectives with H $$\ddot{\text {o}}$$ o ¨ lder-continuous gradients). All the above results are guaranteed with a high probability for heavy-tailed data. Numerical experiments are conducted to justify the theoretical improvement.

Synchronous parallel tasks are widely used in HPC for purchasing high average performance, but merely consider how to guarantee good timing predictabilities. OpenMP is a promising framework for multi-core real-time embedded systems. The synchronous OpenMP tasks are significantly more difficult to schedule and analyze due to constraints posed by OpenMP specifications. An important OpenMP feature is tied task, which must execute on the same thread during the whole life cycle. This paper designs a novel method, called group scheduling, to schedule synchronous OpenMP tasks, which divides tasks into several groups, and assigns some of them to dedicated cores, in order to isolate tied tasks. We derive a linear-time computable response time bound. Experiments with both randomly generated and realistic OpenMP tasks show that our new bound significantly outperforms the existing bound.