Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

CoNeT-GIANT: A compressed Newton-type fully distributed optimization algorithm

Souvik Das, Subhrakanti Dey

TL;DR

This work addresses distributed optimization under limited communication by developing CoNet-GIANT, a fully distributed Newton-type method that incorporates gradient tracking and a compression module. By allowing general compression operators with error-feedback and maintaining Newton-type updates, the method achieves linear convergence with per-iteration communication cost of $O(np)$, comparable to first-order methods. The authors provide a rigorous convergence analysis establishing linear rates under standard smoothness and strong convexity assumptions and demonstrate superior communication efficiency in experiments on synthetic ridge regression and the CovType dataset, relative to gradient-based and Hessian-compressed baselines. This approach offers a practical, scalable solution for high-dimensional distributed learning over wireless networks, where communication is a critical bottleneck.

Abstract

Compression techniques are essential in distributed optimization and learning algorithms with high-dimensional model parameters, particularly in scenarios with tight communication constraints such as limited bandwidth. This article presents a communication-efficient second-order distributed optimization algorithm, termed as CoNet-GIANT, equipped with a compression module, designed to minimize the average of local strongly convex functions. CoNet-GIANT incorporates two consensus-based averaging steps at each node: gradient tracking and approximate Newton-type iterations, inspired by the recently proposed Network-GIANT. Under certain sufficient conditions on the step size, CoNet-GIANT achieves significantly faster linear convergence, comparable to that of its first-order counterparts, both in the compressed and uncompressed settings. CoNet-GIANT is efficient in terms of data usage, communication cost, and run-time, making it a suitable choice for distributed optimization over a wide range of wireless networks. Extensive experiments on synthetic data and the widely used CovType dataset demonstrate its superior performance.

CoNeT-GIANT: A compressed Newton-type fully distributed optimization algorithm

TL;DR

This work addresses distributed optimization under limited communication by developing CoNet-GIANT, a fully distributed Newton-type method that incorporates gradient tracking and a compression module. By allowing general compression operators with error-feedback and maintaining Newton-type updates, the method achieves linear convergence with per-iteration communication cost of , comparable to first-order methods. The authors provide a rigorous convergence analysis establishing linear rates under standard smoothness and strong convexity assumptions and demonstrate superior communication efficiency in experiments on synthetic ridge regression and the CovType dataset, relative to gradient-based and Hessian-compressed baselines. This approach offers a practical, scalable solution for high-dimensional distributed learning over wireless networks, where communication is a critical bottleneck.

Abstract

Compression techniques are essential in distributed optimization and learning algorithms with high-dimensional model parameters, particularly in scenarios with tight communication constraints such as limited bandwidth. This article presents a communication-efficient second-order distributed optimization algorithm, termed as CoNet-GIANT, equipped with a compression module, designed to minimize the average of local strongly convex functions. CoNet-GIANT incorporates two consensus-based averaging steps at each node: gradient tracking and approximate Newton-type iterations, inspired by the recently proposed Network-GIANT. Under certain sufficient conditions on the step size, CoNet-GIANT achieves significantly faster linear convergence, comparable to that of its first-order counterparts, both in the compressed and uncompressed settings. CoNet-GIANT is efficient in terms of data usage, communication cost, and run-time, making it a suitable choice for distributed optimization over a wide range of wireless networks. Extensive experiments on synthetic data and the widely used CovType dataset demonstrate its superior performance.

Paper Structure

This paper contains 17 sections, 6 theorems, 89 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem formulation and notations
  3. Problem description
  4. Standing assumptions
  5. Compression operators
  6. $\textsc{CoNet-GIANT}$ and its analysis
  7. Key steps of $\textsc{CoNet-GIANT}$
  8. Convergence analysis
  9. Experiments
  10. Compression schemes used
  11. Ridge regression with synthetic data
  12. Binary logistic classification
  13. Conclusion
  14. Proofs
  15. Technical results
  16. ...and 2 more sections

Key Result

Lemma 3.1

Consider Algorithm alg:sec_ord_comp along with its associated data and notations established in §sec:algo. Suppose that Assumptions assum:on graph and assum:Standard assumptions hold. Let $W$ be the consensus weight matrix. Define the vector of errors $e(t) \coloneqq \bigl(e_{\mathrm{o}}(t) \; e_{\m for $1 < \tau_{x} < \frac{1}{1 - \alpha_{x} r \delta}$, $1 < \tau_{s} < \frac{1}{1 - \alpha_{s} r \

Figures (3)

  • Figure 1: Figures \ref{['subfig:qnb_con']}-\ref{['subfig:qnb_gt']} compare the errors admitted by $\textsc{CoNet-GIANT}$, $\textsc{C-GT}$, Network-GIANT, and Qu-Li ref:GQ-NL-17 for qNbB-Q compression scheme. Figure \ref{['subfig:qnb_residual']} plots the optimality gaps in terms of the functional values of the global objective function.
  • Figure 2: Figure \ref{['subfig:fc_qnbb_cov']}–\ref{['subfig:fc_ns_cov']} compare $\textsc{CoNet-GIANT}$ with $\textsc{C-GT}$, $\textsc{LEAD}$, $\textsc{COLD}$, and $\textsc{Comp-Hessian}$ under different schemes for the ring network. Figure \ref{['subfig:fc_acc_cov']} summarizes the accuracy attained by these algorithms.
  • Figure 3: Comparison of $\textsc{CoNet-GIANT}$ with $\textsc{C-GT}$, $\textsc{LEAD}$, $\textsc{COLD}$, and $\textsc{Comp-Hessian}$, for the expander network.

Theorems & Definitions (13)

  • Definition 2.1
  • Remark 2.1
  • Lemma 3.1
  • Theorem 3.1
  • proof
  • Remark 3.1: On the linear rate of convergence
  • Theorem 3.2
  • Lemma A.1
  • proof
  • Lemma A.2
  • ...and 3 more