8000 GitHub - TrueNobility303/LEN: [ICLR 2025 Oral] Second-Order Min-Max Optimization with Lazy Hessians.
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LEN (Lazy Extra Newton)

Before running the codes, create the following folders if they do not exist

mkdir img
mkdir result

Synthetic Problem

Experiment on the cubic regularized bilinear min-max problem of the form

$$ \min_{x \in \mathbb{R}^n} \max_{y \in \mathbb{R}^n} f(x,y) = \frac{\rho}{6} \Vert x \Vert^3 + y^\top (A x - b). $$

Reproduce our results via

python -u Synthetic.py --n 10 --training_time 10.0
python -u Synthetic.py --n 100 --training_time 50.0
python -u Synthetic.py --n 100 --training_time 80.0

You are also encouraged to vary the hyper-parameters to see their performance.

Fairness Machine Learning

The objective is given by

$$ \min_{x \in \mathbb{R}^{d_x}} \max_{y \in \mathbb{R}} \frac{1}{n} \sum_{i=1}^n \ell(b_i a_i^\top x) - \beta \ell(c_i y a_i^\top x) + \lambda \Vert x \Vert^2 -\gamma y^2. $$

Create a new folder

mkdir Data

Download the dataset from the links: adult , lawschool, and put them in the created folder.

Reproduce our results via

python -u Fairness.py --rho 10.0 --dataset heart --training_time 10.0
python -u Fairness.py --rho 10.0 --dataset adult --training_time 500.0
python -u Fairness.py --rho 10.0 --dataset lawschool --training_time 5000.0

When the program is completed, the results will be stored in the folder ./result.

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