Tuning Stochastic Gradient Algorithms for Statistical Inference via Large-Sample Asymptotics

Jeffrey Negrea; Jun Yang; Haoyue Feng; Daniel M. Roy; Jonathan H. Huggins

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arXiv · 2207.12395

Tuning Stochastic Gradient Algorithms for Statistical Inference via Large-Sample Asymptotics

Jeffrey Negrea·Jun Yang·Haoyue Feng·Daniel M. Roy·Jonathan H. Huggins

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Abstract

The tuning of stochastic gradient algorithms (SGAs) for optimization and sampling is often based on heuristics and trial-and-error rather than generalizable theory. We address this theory--practice gap by characterizing the large-sample statistical asymptotics of SGAs via a joint step-size--sample-size scaling limit. We show that iterate averaging with a large fixed step size is robust to the choice of tuning parameters and asymptotically has covariance proportional to that of the MLE sampling distribution. We also prove a Bernstein--von Mises-like theorem to guide tuning, including for generalized posteriors that are robust to model misspecification. Numerical experiments validate our results and recommendations in realistic finite-sample regimes. Our work lays the foundation for a systematic analysis of other stochastic gradient Markov chain Monte Carlo algorithms for a wide range of models.

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BibTeX RIS

Jeffrey Negrea, Jun Yang, Haoyue Feng, Daniel M. Roy, Jonathan H. Huggins. 2022-07-25. Tuning Stochastic Gradient Algorithms for Statistical Inference via Large-Sample Asymptotics. https://arxiv.org/abs/2207.12395

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