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Adaptive pruning-based Newton's method for distributed learning

Shuzhen Chen, Yuan Yuan, Youming Tao, Tianzhu Wang, Zhipeng Cai, Dongxiao Yu

TL;DR

This work addresses the practicality of Newton's method for distributed learning in heterogeneous environments by introducing Distributed Adaptive Newton Learning (DANL). DANL initializes the Hessian once and employs pruning-based, region-wise sub-models to adapt training to limited resources, while a server-side aggregation leverages the latest region updates to approximate current region updates. The authors prove a linear convergence rate with a rate of up to (1/2)^t under standard stochastic optimization assumptions and demonstrate robustness to condition number and reduced parameter tuning. Empirical results on logistic regression tasks across multiple LibSVM datasets show fast convergence with efficient communication and resilience to data and worker heterogeneity. The approach enables scalable, second-order distributed optimization suitable for edge, federated, and other resource-constrained settings.

Abstract

Newton's method leverages curvature information to boost performance, and thus outperforms first-order methods for distributed learning problems. However, Newton's method is not practical in large-scale and heterogeneous learning environments, due to obstacles such as high computation and communication costs of the Hessian matrix, sub-model diversity, staleness of training, and data heterogeneity. To overcome these obstacles, this paper presents a novel and efficient algorithm named Distributed Adaptive Newton Learning (\texttt{DANL}), which solves the drawbacks of Newton's method by using a simple Hessian initialization and adaptive allocation of training regions. The algorithm exhibits remarkable convergence properties, which are rigorously examined under standard assumptions in stochastic optimization. The theoretical analysis proves that \texttt{DANL} attains a linear convergence rate while efficiently adapting to available resources and keeping high efficiency. Furthermore, \texttt{DANL} shows notable independence from the condition number of the problem and removes the necessity for complex parameter tuning. Experiments demonstrate that \texttt{DANL} achieves linear convergence with efficient communication and strong performance across different datasets.

Adaptive pruning-based Newton's method for distributed learning

TL;DR

This work addresses the practicality of Newton's method for distributed learning in heterogeneous environments by introducing Distributed Adaptive Newton Learning (DANL). DANL initializes the Hessian once and employs pruning-based, region-wise sub-models to adapt training to limited resources, while a server-side aggregation leverages the latest region updates to approximate current region updates. The authors prove a linear convergence rate with a rate of up to (1/2)^t under standard stochastic optimization assumptions and demonstrate robustness to condition number and reduced parameter tuning. Empirical results on logistic regression tasks across multiple LibSVM datasets show fast convergence with efficient communication and resilience to data and worker heterogeneity. The approach enables scalable, second-order distributed optimization suitable for edge, federated, and other resource-constrained settings.

Abstract

Newton's method leverages curvature information to boost performance, and thus outperforms first-order methods for distributed learning problems. However, Newton's method is not practical in large-scale and heterogeneous learning environments, due to obstacles such as high computation and communication costs of the Hessian matrix, sub-model diversity, staleness of training, and data heterogeneity. To overcome these obstacles, this paper presents a novel and efficient algorithm named Distributed Adaptive Newton Learning (\texttt{DANL}), which solves the drawbacks of Newton's method by using a simple Hessian initialization and adaptive allocation of training regions. The algorithm exhibits remarkable convergence properties, which are rigorously examined under standard assumptions in stochastic optimization. The theoretical analysis proves that \texttt{DANL} attains a linear convergence rate while efficiently adapting to available resources and keeping high efficiency. Furthermore, \texttt{DANL} shows notable independence from the condition number of the problem and removes the necessity for complex parameter tuning. Experiments demonstrate that \texttt{DANL} achieves linear convergence with efficient communication and strong performance across different datasets.
Paper Structure (12 sections, 5 theorems, 48 equations, 2 figures)

This paper contains 12 sections, 5 theorems, 48 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model
  4. Distributed learning with Newton's method
  5. Resource-adaptive learning via pruning
  6. Other notations
  7. Algorithm
  8. Convergence results
  9. Experiments
  10. Parameter setting
  11. Impact of key factors
  12. Appendix

Key Result

lemma thmcounterlemma

For the projected Hessian $[\mathbf{\Pi}]_{\mu }$ computed according to Definition definiton:projection, we have

Figures (2)

  • Figure 1: The impact of $\psi^*$ and $S^{*}$ of DANL
  • Figure 2: The impact of $\psi^*$ and $\gamma_t$ of DANL

Theorems & Definitions (14)

  • definition thmcounterdefinition: Projection 2DBLP:conf/icml/SafaryanIQR22
  • definition thmcounterdefinition: Lipschitz
  • definition thmcounterdefinition: Bounded variance
  • definition thmcounterdefinition: Strong convexity
  • lemma thmcounterlemma
  • proof
  • lemma thmcounterlemma
  • lemma thmcounterlemma
  • lemma thmcounterlemma
  • theorem thmcountertheorem
  • ...and 4 more