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Orthant Based Proximal Stochastic Gradient Method for ℓ1-Regularized Optimization

PyTorch Implementation of non-convex experiments in "Orthant Based Proximal Stochastic Gradient Method for ℓ1-Regularized Optimization", appearing in ECML-PKDD 2020.

[paper] [arXiv]

Abstract

Sparsity-inducing regularization problems are ubiquitous in machine learning applications, ranging from feature selection to model compression. In this paper, we present a novel stochastic method -- Orthant Based Proximal Stochastic Gradient Method (OBProx-SG) -- to solve perhaps the most popular instance, i.e., the l1-regularized problem. The OBProx-SG method contains two steps: (i) a proximal stochastic gradient step to predict a support cover of the solution; and (ii) an orthant step to aggressively enhance the sparsity level via orthant face projection. Compared to the state-of-the-art methods, e.g., Prox-SG, RDA and Prox-SVRG, the OBProx-SG not only converges to the global optimal solutions (in convex scenario) or the stationary points (in non-convex scenario), but also promotes the sparsity of the solutions substantially. Particularly, on a large number of convex problems, OBProx-SG outperforms the existing methods comprehensively in the aspect of sparsity exploration and objective values. Moreover, the experiments on non-convex deep neural networks, e.g., MobileNetV1 and ResNet18, further demonstrate its superiority by achieving the solutions of much higher sparsity without sacrificing generalization accuracy.

Requirements

• torch: 1.4.0 or higher
• torchvision: 0.5.0 or higher

Please follow the instructions here to install PyTorch.

Set up Dataset

In datasets.py, DATA_DIRrepresents the path to dataset. Please replace this constant variable with the path to the dataset.

Running Code

Run all experiments

The scripts of running all non-convex experiments are provided in the command.sh. You can simply run the following command to test non-convex experiments:

bash command.sh

Run specific experiment

• optimizer: [ obproxsg | obproxsg_plus | proxsg | rda | proxsvrg ]
• model: [ mobilenetv1 | resnet18 ]
• dataset_name: [ cifar10 | fashion_mnist ]

python run.py --optimizer <optimizer> \
              --model <model> \
              --dataset_name <dataset_name> \
              --lambda_ 0.0001 \
              --max_epoch 200 \
              -lr 0.1 \
              --batch_size 128

An example is:

python run.py --optimizer obproxsg_plus \
              --model mobilenetv1 \
              --dataset_name cifar10 \
              --lambda_ 0.0001 \
              --max_epoch 200 \
              -lr 0.1 \
              --batch_size 128

Evaluation

To evaluate our model, users can run the following command to evaluate the trained model. Make sure that the arguments match the training information of trained model.

python evaluate.py --model <model> \
                   --dataset_name <dataset_name> \
                   --lambda_ 0.0001 \
                   --ckpt <ckpt>

An example is:

python evaluate.py --model resnet18 \
                   --dataset_name cifar10 \
                   --lambda_ 0.0001 \
                   --ckpt checkpoints/obproxsg_plus_resnet18_cifar10_1.000000E-04.pt

Citation

If you find the code or results useful, please kindly cite the following paper:

@inproceedings{chen2021orthant,
  title={Orthant Based Proximal Stochastic Gradient Method for $\ell_1 $-Regularized Optimization},
  author={Chen, Tianyi and Ding, Tianyu and Ji, Bo and Wang, Guanyi and Shi, Yixin and Tian, Jing and Yi, Sheng and Tu, Xiao and Zhu, Zhihui},
  booktitle={Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2020, Ghent, Belgium, September 14--18, 2020, Proceedings, Part III},
  pages={57--73},
  year={2021},
  organization={Springer International Publishing}
}

or

@article{chen2020orthant,
  title={Orthant Based Proximal Stochastic Gradient Method for $\ell_1 $-Regularized Optimization},
  author={Chen, Tianyi and Ding, Tianyu and Ji, Bo and Wang, Guanyi and Tian, Jing and Shi, Yixin and Yi, Sheng and Tu, Xiao and Zhu, Zhihui},
  journal={arXiv preprint arXiv:2004.03639},
  year={2020}
}