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Which Algorithmic Choices Matter at Which Batch Sizes? Insights From a Noisy Quadratic Model (1907.04164v2)

Published 9 Jul 2019 in cs.LG and stat.ML

Abstract: Increasing the batch size is a popular way to speed up neural network training, but beyond some critical batch size, larger batch sizes yield diminishing returns. In this work, we study how the critical batch size changes based on properties of the optimization algorithm, including acceleration and preconditioning, through two different lenses: large scale experiments, and analysis of a simple noisy quadratic model (NQM). We experimentally demonstrate that optimization algorithms that employ preconditioning, specifically Adam and K-FAC, result in much larger critical batch sizes than stochastic gradient descent with momentum. We also demonstrate that the NQM captures many of the essential features of real neural network training, despite being drastically simpler to work with. The NQM predicts our results with preconditioned optimizers, previous results with accelerated gradient descent, and other results around optimal learning rates and large batch training, making it a useful tool to generate testable predictions about neural network optimization.

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Authors (8)
  1. Guodong Zhang (41 papers)
  2. Lala Li (11 papers)
  3. Zachary Nado (23 papers)
  4. James Martens (20 papers)
  5. Sushant Sachdeva (49 papers)
  6. George E. Dahl (27 papers)
  7. Christopher J. Shallue (16 papers)
  8. Roger Grosse (68 papers)
Citations (140)

Summary

Analysis of Optimization Algorithms and Batch Sizes in Neural Network Training

The paper "Which Algorithmic Choices Matter at Which Batch Sizes? Insights From a Noisy Quadratic Model" explores how various aspects of optimization algorithms affect the critical batch size in neural network training. Specifically, the paper investigates how preconditioning, acceleration, and averaging influence critical batch sizes, utilizing both empirical experimentation and theoretical analysis through a noisy quadratic model (NQM).

The motivation behind this research stems from the increasing use of larger batch sizes to expedite neural network training on data parallel hardware. Larger batch sizes can improve gradient estimates and reduce the number of training steps, but only up to a point. Due to practical constraints, there is a critical batch size beyond which greater batch sizes produce diminishing returns. Previous work has identified this phenomenon but focused primarily on stochastic gradient descent (SGD) and its variants. This paper aims to extend the understanding of these batch size effects to other optimizers.

Empirical tests demonstrated that the use of preconditioned optimizers such as Adam and K-FAC significantly increases the critical batch size compared to SGD with momentum. The NQM was effective in capturing essential behaviors of neural network training and provided insights consistent with observed results. The analysis confirmed that the NQM's predictions align with large scale experiments regarding preconditioned optimizers, accelerated gradient descent, and optimal learning rates in large batch training.

Key experimental findings include:

  • The critical batch size is greater for preconditioned optimizers like Adam and K-FAC compared to SGD with momentum. This highlights the significant influence of preconditioning in extending batch size scalability.
  • Exponential moving averages reduced the number of training steps required for a given batch size, achieving acceleration even at smaller batch sizes and thereby conserving computational resources.
  • Momentum provides no benefit over plain SGD for small batch sizes but increases the effective critical batch size in large batch scenarios.
  • Preconditioned optimizers can enhance training efficiency even at minimal batch sizes, providing advantages across a broader spectrum of tasks.

The NQM's advantages lie in its simplicity and capability to run simulations swiftly, making it a practical tool for generating testable predictions about neural network optimization. Furthermore, the research underscores the importance of selecting optimization algorithms in the context of desired batch sizes, offering a more nuanced understanding of batch size effects in deep learning.

The implications of these findings are both practical and theoretical. Practically, they inform better decision-making regarding the choice of optimizers and appropriate batch sizes in real-world AI deployments, potentially reducing training time and computational costs. Theoretically, the alignment of NQM predictions with empirical results supports the efficacy of simplified models in understanding complex neural network behaviors.

Future developments in AI could explore more advanced models for optimization dynamics, addressing potential limitations or extensions of the NQM, and further investigate the underlying mechanisms that enable certain optimizers to handle larger batch sizes more effectively. Continued research in this area will enhance understanding and contribute to the optimization of neural network training processes, potentially leading to advances in efficiency and capability across various AI applications.