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We study an easy-to-implement algorithm to construct asymptotically valid confidence regions for model parameters in stochastic gradient descent. The main idea is to cancel out the covariance matrix which is hard/costly to estimate using the batch means method with a fixed number of batches. In developing the algorithm, we establish a process-level functional central limit theorem for Polyak-Ruppert averaging iterates. We also extend the batch means method to accommodate more general batch size specifications.

On Constructing Confidence Region for Model Parameters in Stochastic Gradient Descent Via Batch Means