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

• URL: http://arxiv.org/abs/2207.12395v3
• Date: Thu, 20 Jul 2023 16:21:58 GMT
• Title: Tuning Stochastic Gradient Algorithms for Statistical Inference via Large-Sample Asymptotics
• Authors: Jeffrey Negrea, Jun Yang, Haoyue Feng, Daniel M. Roy, Jonathan H. Huggins
• Abstract summary: tuning of gradient algorithms often based on trial-and-error rather than generalizable theory. We show that averaging with a large fixed step size is robust to the choice of tuning parameters. We lay the foundation for a systematic analysis of other gradient Monte Carlo algorithms.
• Score: 18.93569692490218
• License: http://creativecommons.org/licenses/by/4.0/
• 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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