Distributed Dual Coordinate Ascent with Imbalanced Data on a General Tree Network

In this paper, we investigate the impact of imbalanced data on the convergence of distributed dual coordinate ascent in a tree network for solving an empirical loss minimization problem in distributed machine learning. To address this issue, we propose a method called delayed generalized distributed dual coordinate ascent that takes into account the information of the imbalanced data, and provide the analysis of the proposed algorithm. Numerical experiments confirm the effectiveness of our proposed method in improving the convergence speed of distributed dual coordinate ascent in a tree network.Comment: To be published in IEEE 2023 Workshop on Machine Learning for Signal Processing (MLSP

A dual ascent framework for Lagrangean decomposition of combinatorial problems

We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to multiple problem types. In this work, we propose such a general algorithm. It depends on several parameters, which can be used to optimize its performance in each particular setting. We demonstrate efficacy of our method on graph matching and multicut problems, where it outperforms state-of-the-art solvers including those based on subgradient optimization and off-the-shelf linear programming solvers

A dual ascent framework for Lagrangean decomposition of combinatorial problems

We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to multiple problem types. In this work, we propose such a general algorithm. It depends on several parameters, which can be used to optimize its performance in each particular setting. We demonstrate efficacy of our method on graph matching and multicut problems, where it outperforms state-of-the-art solvers including those based on subgradient optimization and off-the-shelf linear programming solvers

Smoothing Proximal Gradient Method for General Structured Sparse Learning

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, based on the l1/l2 mixed-norm penalty, and 2) graph-guided fusion penalty. For both types of penalties, due to their non-separability, developing an efficient optimization method has remained a challenging problem. In this paper, we propose a general optimization approach, called smoothing proximal gradient method, which can solve the structured sparse regression problems with a smooth convex loss and a wide spectrum of structured-sparsity-inducing penalties. Our approach is based on a general smoothing technique of Nesterov. It achieves a convergence rate faster than the standard first-order method, subgradient method, and is much more scalable than the most widely used interior-point method. Numerical results are reported to demonstrate the efficiency and scalability of the proposed method.Comment: arXiv admin note: substantial text overlap with arXiv:1005.471