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

\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

X = [x_1^\top, \dots, x_n^\top]^\top \in \mathbb{R}^{n \times p}

and

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

This benchmark can be run using the following commands:

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

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

$ benchopt run benchmark_huber_l2 -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.