Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD has only been recently studied, yet is important due to the growing need for uncertainty quantification. We investigate two computationally cheap resampling-based methods to construct confidence intervals for SGD solutions. One uses multiple, but few, SGDs in parallel via resampling with replacement from the data, and another operates this in an online fashion. Our methods can be regarded as enhancements of established bootstrap schemes to substantially reduce the computation effort in terms of resampling requirements, while at the same time bypassing the intricate mixing conditions in existing batching methods. We achieve these via a recent so-called cheap bootstrap idea and Berry-Esseen-type bound for SGD.

通过采用分别基于重采样的多个随机梯度下降和在线方法，我们实现了对于随机梯度下降解的置信区间的构建，通过最近被称为廉价引导思想和SGD的Berry-Esseen型界限，我们显著减少了计算量，并绕过了现有分批方法中复杂的混合条件。

高效不确定性量化: 简易重采样随机梯度下降