In stochastic optimization, a common tool to deal sequentially with large sample is to consider the well-known stochastic gradient algorithm. Nevertheless, since the stepsequence is the same for each direction, this can lead to bad results in practice in case of ill-conditionned problem. To overcome this, adaptive gradient algorithms such that Adagrad or Stochastic Newton algorithms should be prefered. This paper is devoted to the non asymptotic analyis of these adaptive gradient algorithms for strongly convex objective. All the theoretical results will be adapted to linear regression and regularized generalized linear model for both Adagrad and Stochastic Newton algorithms.

翻译：在随机优化中，处理大样本序列的常用工具是著名的随机梯度算法。然而，由于步长序列在每个方向上相同，在面对病态问题时，这可能导致实际效果不佳。为克服这一局限，应优先采用自适应梯度算法，如Adagrad或随机牛顿算法。本文致力于对强凸目标函数的自适应梯度算法进行非渐近分析。所有理论结果将适用于线性回归和正则化广义线性模型，并涵盖Adagrad与随机牛顿算法两种情况。