Statistical Inference for Stochastic Gradient Descent: Beyond Finite Variance
Stochastic gradient descent (SGD) is foundational to large-scale statistical learning and stochastic optimization. However, in some modern statistical learning problems, stochastic gradients can exhibit infinite-variance behavior. Consequently, classical inference methods for SGD that rely on a finite-variance assumption break down. We develop a model-agnostic methodology for constructing confidence regions from SGD iterates in both the finite- and infinite-variance regimes. We first show that Polyak--Ruppert averaging has an asymptotic directional scale no larger than that of the fastest-rate final iterate, analogous to its lower asymptotic variance in the finite-variance setting. Accord...
| Authors | Jose Blanchet, Peter Glynn, Wenhao Yang |
|---|---|
| Primary category | stat.ML |
| Published | 25 May 2026 |
| Last updated at source | 30 July 2026 |
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