A proximal forward-backward splitting based algorithmic framework for Wasserstein logistic regression using heavy ball strategy

ABSTRACT

In this paper, a forward-backward splitting based algorithmic framework incorporating the heavy ball strategy is proposed so as to efficiently solve the Wasserstein logistic regression problem. The proposed algorithmic framework consists two phases: the first phase involves a gradient descent step extension method, whilst the second phase involves a problem of instantaneous optimisation which balances the minimisation of a regularisation term while maintaining close proximity to the interim state given in the first phase. Then, it proves that the proposed algorithmic framework converges to the optimal solution of the Wasserstein logistic regression problem. Finally, numerical experiments are conducted, which illustrate the efficient implementation for high-dimensional sparsity data. The numerical results demonstrate that the proposed algorithmic framework outperforms not only the off-the-shelf solvers, but also some existing first-order algorithms.

KEYWORDS:

• Wasserstein logistic regression
• forward-backward splitting
• heavy ball strategy

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from https://www.csie.ntu.edu.tw/∼cjlin/libsvmtools/datasets/.

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China [grant number 61803056], in part by the Science and Technology Research Program of Education Commission of Chongqing [grant number KJZD-M202100701], in part by the Joint Training Base Construction Project for Graduate Students in Chongqing [grant number JDLHPYJD2021016], and in part by the Program of Chongqing Innovation Team Project in University [grant number CXTDX201601022].