Distributed inexact Newton method with adaptive step sizes
Dušan Jakovetić1, Nataša Krejić1, Greta Malaspina2
1Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, Novi Sad, 21000 Serbia.
Computational Optimization and Applications
|May 20, 2025
Summary
A new method called DINAS (Distributed Inexact Newton method with Adaptive step size) speeds up distributed optimization. It achieves faster convergence for personalized and consensus optimization problems with less data sharing.
Area of Science:
- Distributed optimization
- Networked systems
- Machine learning
Background:
- Distributed optimization is crucial for large-scale problems.
- Existing methods face challenges with communication and computation costs.
Purpose of the Study:
- Introduce a novel method, DINAS (Distributed Inexact Newton method with Adaptive step size).
- Improve efficiency and reduce communication overhead in distributed optimization.
Main Methods:
- DINAS uses adaptive step sizes and reduced global parameter knowledge.
- It avoids local Hessian inverse calculations and Hessian communications.
- Convergence analysis for inexact Newton methods with adaptive step sizes is provided.
Main Results:
- DINAS achieves quadratic convergence (computation) and linear convergence (communication) for personalized optimization.
- The communication convergence rate is independent of network topology and local function conditions.
- DINAS converges to the global solution for consensus optimization problems.
- Numerical experiments show significant improvements over existing methods.
Conclusions:
- DINAS offers a more efficient and practical approach to distributed optimization.
- The method is robust across different network structures and problem complexities.
- Provides theoretical insights into adaptive step size methods.
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