A Manifold-Aware Distributed Proximal Quasi-Newton Method for Regularized Optimization

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# MADPQN - A Manifold-Aware Distributed Proximal Quasi-Newton Method for Regularized Optimization

This code implements the algorithm proposed in the following paper in C/C++ and MPI: LI Yu-Sheng, CHIANG Wei-Lin, LEE Ching-pei. Manifold Identification for Ultimately Communication-Efficient Distributed Optimization. The 37th International Conference on Machine Learning, 2020.

## Getting started

To compile the code, you will need to install g++, and an implementation of MPI. You will need to list the machines being used in a separate file, and make sure they are directly accessible through ssh. Additionally the code depends on the BLAS and LAPACK libraries.

The code split.py, borrowed from MPI-LIBLINEAR, partition the data and distribted the segments to the designated machines. Then the program ./train solves the optimization problem to obtain a model.

## Problem being solved

The code solves (1): the L1-regularized logistic regression problem.

min_{w} |w|1 + C \sum{i=1}^n \log(1 + \exp(- y_i w^T x_i))

with a user-specified parameter C > 0,

(2): the L1-Regularized least-sqaure regression (LASSO) problem.

min_{w} |w|1 + C \sum{i=1}^n (w^T x_i - y_i)^2 / 2.

with a user-specified parameter C > 0,

(3): the L1-regularized L2-loss support vector classification problem.

min_{w} |w|1 + C \sum{i=1}^n \max{0,1 - y_i w^T x_i, 0}^2.

with a user-specified parameter C > 0,

and (4): the GroupLASSO-regularized multinomial logistic regression problem for multi-class classification.

A Manifold-Aware Distributed Proximal Quasi-Newton Method for Regularized Optimization

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