Second order methods for minimax optimization

This repo includes code for running first- and second-order methods for minimax optimization in Newton-type Methods for Minimax Optimization, including gradient descent ascent (GDA), total gradient descent ascent (TGDA), follow-the-ridge (FR), gradient-descent Newton (GDN) and complete Newton (CN). We run these algorithms on tasks including estimation of a single Gaussian, learning a mixture of Gaussians, and generating digits on the MNIST 0/1 subset. GPU/CUDA required for running all our experiments.

• model.py contains different neural net architectures for various tasks
• data.py generates various datasets
• run.py is the main python script for comparing different algorithms
• utils.py implements various helper functions including hessian-vector-product and conjugate gradient.

Scripts for running the experiments

The following bash files include configurations to run various experiments. You can uncomment different parts to run different algorithms including GDA/TGDA/FR/GDN/CN.

• bash_gaussian_mean.sh: estimation of the mean of a Gaussian
• bash_gaussian_covariance.sh: estimation of the covariance of a Gaussian
• bash_gmm.sh: learning a mixture of Gaussians
• bash_gmm.sh: learning to generate digits in MNIST 0/1 dataset

Pretrained models

The folder ./checkpoints includes two pretrained models for GMM and MNIST separately. We used the model trained by GDA as initialization.

Plot files

• plot_gmm.py: plot file for visualizing the Gaussian mixtures generated by different algorithms
• plot_mnist.py: plot file for visualizing the digits generated generated by different algorithms

If you want to use our code, please add the following reference:

@inproceedings{zhang2020newton,
  title={Newton-type methods for minimax optimization},
  author={Zhang, Guojun and Wu, Kaiwen and Poupart, Pascal and Yu, Yaoliang},
  booktitle={ICML Workshop on Beyond first-order methods in ML systems},
  year={2021},
  url={https://arxiv.org/abs/2006.14592}
}