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BADM: Batch ADMM for Deep Learning

Ouya Wang, Shenglong Zhou, Geoffrey Ye Li

TL;DR

BADM tackles slow convergence in stochastic DL optimization by introducing a data-driven batch-ADMM framework that partitions data into batches and sub-batches, enabling parallel primal/dual updates and global parameter aggregation. The method formulates an augmented Lagrangian with local and global variables, and uses inexact subproblem solves to maintain computational efficiency comparable to SGD while enabling parallelism. A rigorous convergence analysis under $L$-smoothness and bounded sampling bias yields a sublinear rate $\min_{k} \|\nabla F(\mathbf{z}^k)\|^2 = O(\delta + 1/K)$, with $\delta=0$ (single batch) recovering the $O(1/K)$ rate. Empirically, BADM consistently outperforms standard optimizers across graph modelling, vision, generative modelling, and NLP, delivering higher accuracy, faster convergence, and reduced training time, demonstrating the method’s practical impact for scalable DL training.

Abstract

Stochastic gradient descent-based algorithms are widely used for training deep neural networks but often suffer from slow convergence. To address the challenge, we leverage the framework of the alternating direction method of multipliers (ADMM) to develop a novel data-driven algorithm, called batch ADMM (BADM). The fundamental idea of the proposed algorithm is to split the training data into batches, which is further divided into sub-batches where primal and dual variables are updated to generate global parameters through aggregation. We evaluate the performance of BADM across various deep learning tasks, including graph modelling, computer vision, image generation, and natural language processing. Extensive numerical experiments demonstrate that BADM achieves faster convergence and superior testing accuracy compared to other state-of-the-art optimizers.

BADM: Batch ADMM for Deep Learning

TL;DR

BADM tackles slow convergence in stochastic DL optimization by introducing a data-driven batch-ADMM framework that partitions data into batches and sub-batches, enabling parallel primal/dual updates and global parameter aggregation. The method formulates an augmented Lagrangian with local and global variables, and uses inexact subproblem solves to maintain computational efficiency comparable to SGD while enabling parallelism. A rigorous convergence analysis under -smoothness and bounded sampling bias yields a sublinear rate , with (single batch) recovering the rate. Empirically, BADM consistently outperforms standard optimizers across graph modelling, vision, generative modelling, and NLP, delivering higher accuracy, faster convergence, and reduced training time, demonstrating the method’s practical impact for scalable DL training.

Abstract

Stochastic gradient descent-based algorithms are widely used for training deep neural networks but often suffer from slow convergence. To address the challenge, we leverage the framework of the alternating direction method of multipliers (ADMM) to develop a novel data-driven algorithm, called batch ADMM (BADM). The fundamental idea of the proposed algorithm is to split the training data into batches, which is further divided into sub-batches where primal and dual variables are updated to generate global parameters through aggregation. We evaluate the performance of BADM across various deep learning tasks, including graph modelling, computer vision, image generation, and natural language processing. Extensive numerical experiments demonstrate that BADM achieves faster convergence and superior testing accuracy compared to other state-of-the-art optimizers.
Paper Structure (17 sections, 2 theorems, 25 equations, 9 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 2 theorems, 25 equations, 9 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. SGD-based learning algorithms
  3. ADM and ADMM-based learning algorithms
  4. Our contribution
  5. Organization
  6. The BADM Algorithm
  7. Notation
  8. Model Description
  9. The algorithmic design
  10. Convergence analysis
  11. Comparison with other algorithms
  12. Evaluation of BADM
  13. Graph modelling
  14. Computer vision
  15. Image generation
  16. ...and 2 more sections

Key Result

Lemma 2.1

Let ${(\textbf{w}^\ell,\{(\textbf{w}_{bs}^\ell,{\boldsymbol \pi}_{bs}^\ell):(b,s)\in{\mathbb M}\})}$ be the sequence generated by BADM. Under Assumptions assum-Lip and assum-bias, where ${\mathcal{L}}^k$ is defined by

Figures (9)

  • Figure 1: Data split and each epoch of BADM.
  • Figure 2: Training loss v.s. iterations for node classification.
  • Figure 3: Performance of three optimizers.
  • Figure 4: Training loss v.s. iterations for image classifications.
  • Figure 5: Testing KID v.s. iterations by conditional GAN and DDIM.
  • ...and 4 more figures

Theorems & Definitions (2)

  • Lemma 2.1
  • Theorem 2.1