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

TL;DR

This paper introduces a method for constructing valid confidence regions for stochastic gradient descent parameters using batch means, including theoretical guarantees and extensions for various batch sizes.

Contribution

It develops a new algorithm for confidence region construction that avoids covariance estimation and proves a process-level CLT for Polyak-Ruppert averaging SGD estimators.

Findings

Establishes a process-level functional CLT for SGD estimators.

Proposes an extended batch means method for different batch size specifications.

Provides a practical algorithm for confidence region construction in stochastic optimization.

Abstract

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 functional central limit theorem for Polyak-Ruppert averaging based stochastic gradient descent estimators. We also extend the batch means method to accommodate more general batch size specifications.