Statistical Inference for Model Parameters in Stochastic Gradient Descent via Batch Means

Statistical inference of true model parameters based on stochastic gradient descent (SGD) has started receiving attention in recent years. In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method. The main idea is to cancel out the covariance matrix which is hard/costly to estimate. In the process of developing the algorithm, we establish process-level function central limit theorem for Polyak-Ruppert averaging based SGD estimators. We also extend the batch means method to accommodate more general batch size specifications.