Redirecting to original paper in 30 seconds...
Click below to go immediately or wait for automatic redirect
📄 Abstract
Abstract: We consider primal-dual algorithms for general empirical risk minimization
problems in distributed settings, focusing on two prominent classes of
algorithms. The first class is the communication-efficient distributed dual
coordinate ascent (CoCoA), derived from the coordinate ascent method for
solving the dual problem. The second class is the alternating direction method
of multipliers (ADMM), including consensus ADMM, proximal ADMM, and linearized
ADMM. We demonstrate that both classes of algorithms can be transformed into a
unified update form that involves only primal and dual variables. This
discovery reveals key connections between the two classes of algorithms: CoCoA
can be interpreted as a special case of proximal ADMM for solving the dual
problem, while consensus ADMM is equivalent to a proximal ADMM algorithm. This
discovery provides insight into how we can easily enable the ADMM variants to
outperform the CoCoA variants by adjusting the augmented Lagrangian parameter.
We further explore linearized versions of ADMM and analyze the effects of
tuning parameters on these ADMM variants in the distributed setting. Extensive
simulation studies and real-world data analysis support our theoretical
findings.
Authors (4)
Runxiong Wu
Dong Liu
Xueqin Wang
Andi Wang
Submitted
February 1, 2025
Key Contributions
This paper unifies two prominent paradigms in distributed optimization: CoCoA and ADMM. It demonstrates that both can be transformed into a unified update form, revealing that CoCoA is a special case of proximal ADMM for the dual problem, and consensus ADMM is equivalent to proximal ADMM, providing insights for algorithm improvement.
Business Value
Offers a deeper theoretical understanding of distributed optimization algorithms, potentially leading to more efficient and robust training of large-scale machine learning models used in various industries.