# Benchmark repository for optimization¶

BenchOpt is a package to simplify, make more transparent and more reproducible the comparisons of optimization algorithms.

BenchOpt is written in Python but it is available with many programming languages. So far it has been tested with Python, R, Julia and compiled binaries written in C/C++ available via a terminal command. If it can be installed via conda it should just work!

BenchOpt is used through a command line as documented in API Documentation. Ultimately running and replicating an optimization benchmark should be as simple as doing:

$git clone https://github.com/benchopt/benchmark_logreg_l2$ benchopt run ./benchmark_logreg_l2


Running these commands will fetch the benchmark files and give you a benchmark plot on l2-regularized logistic regression:

Learn how to Write a benchmark.

## Install¶

This package can be installed through pip using:

$pip install benchopt  This will install the command line tool to run the benchmark. Then, existing benchmarks can be retrieved from git or created locally. To discover which benchmarks are presently available look for benchmark_* repositories on GitHub, such as for l1-regularized logistic regression. This benchmark can then be retrieved locally with: $ git clone https://github.com/benchopt/benchmark_lasso.git


## Command line usage¶

To run Lasso benchmarks on all datasets and with all solvers, run:

$benchopt run benchmark_lasso  Use $ benchopt run -h


## List of optimization problems available¶

Notation: In what follows, n (or n_samples) stands for the number of samples and p (or n_features) stands for the number of features.

$y \in \mathbb{R}^n, X = [x_1^\top, \dots, x_n^\top]^\top \in \mathbb{R}^{n \times p}$
• ols: ordinary least-squares. This consists in solving the following program:

$\min_w \frac{1}{2} \|y - Xw\|^2_2$
• nnls: non-negative least-squares. This consists in solving the following program:

$\min_{w \geq 0} \frac{1}{2} \|y - Xw\|^2_2$
• lasso: l1-regularized least-squares. This consists in solving the following program:

$\min_w \frac{1}{2} \|y - Xw\|^2_2 + \lambda \|w\|_1$
• logreg_l2: l2-regularized logistic regression. This consists in solving the following program:

$\min_w \sum_i \log(1 + \exp(-y_i x_i^\top w)) + \frac{\lambda}{2} \|w\|_2^2$
• logreg_l1: l1-regularized logistic regression. This consists in solving the following program:

$\min_w \sum_i \log(1 + \exp(-y_i x_i^\top w)) + \lambda \|w\|_1$