We prove new convergence rates for a generalized version of stochastic Nesterov acceleration under interpolation conditions. Unlike previous analyses, our approach accelerates any stochastic gradient method which makes sufficient progress in expectation. The proof, which proceeds using the estimating sequences framework, applies to both convex and strongly convex functions and is easily specialized to accelerated SGD under the strong growth condition. In this special case, our analysis reduces the dependence on the strong growth constant from $\rho$ to $\sqrt{\rho}$ as compared to prior work. This improvement is comparable to a square-root of the condition number in the worst case and address criticism that guarantees for stochastic acceleration could be worse than those for SGD.

我们在插值条件下证明了随机Nesterov加速的新的收敛速度。不同于以往的分析，我们的方法可以加速任何在期望中取得足够进展的随机梯度方法。证明使用估计序列框架进行，适用于凸函数和强凸函数，并且可以轻松推广到满足强生长条件的加速SGD。在这种特殊情况下，我们的分析将强生长常数的依赖性从ρ减小到√ρ，相对于以前的工作来说，这一改进相当于最坏情况下条件数的平方根，并解决了对于随机加速的保证可能不如SGD的批评。

基于插值的随机加速梯度下降算法的快速收敛