An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are efficient candidates. Indeed, (1) they do not need too much computational efforts, (2) they do not need to store all the data, which is crucial when we deal with big data, (3) they allow to simply update the estimates, which is important when data arrive sequentially. The aim of this work is to give asymptotic and non asymptotic rates of convergence of stochastic gradient estimates as well as of their averaged versions when the function we would like to minimize is only locally strongly convex.

翻译：统计中通常存在的一个问题在于估计一个曲线函数的最小化程度。 当我们必须处理在高维空间采集数值的大型样本时, 随机梯度算法及其平均版本是有效的选择。 事实上, (1) 它们不需要太多的计算努力, (2) 它们不需要存储所有数据, 而当我们处理大数据时,这些数据至关重要, (3) 它们允许简单地更新估计数, 而当数据按顺序到达时这一点很重要。 这项工作的目的是在随机梯度估计及其平均版本的趋同率方面做到无药可治和非无药可治。 当我们想要最小化的功能只是局部的非常模糊时, 其平均版本的趋同率就会达到无药可治和非药可治的程度 。