On the Utility of Equal Batch Sizes for Inference in Stochastic Gradient Descent

2024-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Rahul Singh, Abhinek Shukla, and Dootika Vats introduce an equal batch-size (EBS) strategy for inference in Stochastic Gradient Descent (SGD), addressing challenges posed by its Markovian nature. Published in JMLR 26(258) in 2025, their work proposes a memory-efficient alternative to the traditional increasing batch-size approach for constructing a batch-means estimator of the asymptotic covariance matrix. The authors demonstrate that this EBS estimator is consistent under mild conditions and uniquely allows for bias-correction of the variance without additional memory cost. Furthermore, they present marginal-friendly simultaneous confidence intervals for large-dimensional problems and illustrate how ASGD covariance estimators can enhance predictions.

Key takeaway

Research Scientists working with large-scale machine learning models using Stochastic Gradient Descent should consider implementing the equal batch-size strategy. This approach offers a memory-efficient way to estimate asymptotic covariance and correct variance bias, potentially leading to more robust inference and improved prediction accuracy in your models, especially when dealing with high-dimensional data.

Key insights

Equal batch sizes can consistently estimate SGD asymptotic covariance with memory efficiency and bias correction.

Principles

• SGD inference is challenging due to its Markovian nature.
• Averaged SGD (ASGD) allows asymptotic normality for batch-means.
• Bias-correction for variance is possible without extra memory.

Method

The proposed method uses an equal batch-size strategy to construct a consistent batch-means estimator for the asymptotic covariance matrix of averaged SGD, enabling bias-correction for variance and supporting marginal-friendly simultaneous confidence intervals.

In practice

• Employ EBS for memory-efficient SGD inference.
• Apply ASGD covariance for improved predictions.
• Use marginal-friendly CIs for high-dimensional problems.

Topics

• Stochastic Gradient Descent
• Averaged SGD
• Batch-means Estimator
• Statistical Inference
• Covariance Estimation

Code references

• Abhinek-Shukla/SGD-EBS
• JmlrOrg/v26

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.