Benchmark for L2-regularized Huber regression

Benchopt is a package to simplify and make more transparent and reproducible the comparisons of optimization algorithms. This benchmark is dedicated to solver:

$$\min_{w, \sigma} {\sum_{i=1}^n\left(\sigma + H_{\epsilon}\left(\frac{X_{i}w - y_{i}}{\sigma}\right)\sigma\right) + \alpha {\|w\|_2}^2}$$

where $n$ (or n_samples) stands for the number of samples, $p$ (or n_features) stands for the number of features

$$y \in \mathbb{R}^n, \quad X \in \mathbb{R}^{n \times p}$$

and

$$ H_{\epsilon}(z) = \begin{cases} z^2 & \text {if } \vert z \vert < \epsilon, \\ 2 \epsilon \vert z \vert - \epsilon^2 & \text{otherwise} \end{cases} $$

Install

This benchmark can be run using the following commands:

$ pip install -U benchopt
$ git clone https://github.com/benchopt/benchmark_huber_l2
$ cd benchmark_huber_l2
$ benchopt run .

Apart from the problem, options can be passed to benchopt run, to restrict the benchmarks to some solvers or datasets, e.g.:

$ benchopt run . -s sklearn -d simulated --max-runs 10 --n-repetitions 10

Use benchopt run -h for more details about these options, or visit https://benchopt.github.io/api.html.