Benchmarking L2-Regularized Huber Regression for Optimization Algorithms

Benchmarking L2-Regularized Huber Regression for Optimization Algorithms

Recently, the field of optimization algorithms has seen significant advancements, with numerous algorithms claiming superior performance for various problem domains. However, comparing these algorithms objectively can be challenging due to the lack of standardized benchmarking procedures. To address this issue, the benchopt package was developed to simplify and enhance the transparency and reproducibility of optimization algorithm comparisons.

In this article, we focus on the benchmarking of L2-regularized Huber regression, a popular optimization problem in the field of machine learning. The problem can be formulated as follows:

minimize $\sum_{i=1}^n (\sigma + H_{\epsilon}(\frac{X_{i}w – y_{i}}{\sigma})\sigma) + \alpha {\|w\|_2}^2$

where $n$ refers to the number of samples, $p$ represents the number of features, $y \in \mathbb{R}^n$ is the target variable, and $X \in \mathbb{R}^{n \times p}$ is the feature matrix.

To benchmark the performance of optimization algorithms on this problem, we leverage the benchopt package. To get started, follow these installation instructions:

1. Install the benchopt package by running the command pip install -U benchopt.
2. Clone the benchmark_huber_l2 repository by executing git clone https://github.com/benchopt/benchmark_huber_l2.
3. Navigate to the benchmark_huber_l2 directory using the command cd benchmark_huber_l2.
4. Run the benchmark by executing benchopt run ..

The benchmark can be further customized by passing additional options to the benchopt run command. For example, you can restrict the benchmark to specific solvers or datasets using the -s and -d options, respectively. Additionally, you can specify the maximum number of runs and repetitions using the --max-runs and --n-repetitions options.

To learn more about the available options and explore the benchopt package’s API, visit the official documentation at https://benchopt.github.io/api.html.

In conclusion, benchmarking optimization algorithms is crucial for objectively evaluating their performance. By adopting the benchopt package and following the benchmarking procedure outlined in this article, researchers and practitioners can ensure transparency, reproducibility, and a fair comparison between optimization algorithms. The benchopt package facilitates a standardized benchmarking process that benefits the wider optimization community.

We encourage readers to explore the benchmarks, experiment with different solvers and datasets, and contribute to the growing body of knowledge in the field of optimization algorithms.

References:
– benchopt package repository: https://github.com/benchopt/benchmark_huber_l2
– benchopt package documentation: https://benchopt.github.io/api.html

License: MIT License