A Benchmarking Framework for Geometric Random Walks

Sampling from high-dimensional convex polytopes is a fundamental problem with applications in statistics, machine learning, optimization, and systems biology. Modern libraries such as VolEsti provide a rich collection of geometric random walk algorithms; however, there is currently no unified, extensible, and reproducible framework for benchmarking these methods in practice. In my recent MSc thesis, I conducted a large-scale empirical comparison of state-of-the art sampling algorithms across multiple software ecosystems. This work revealed a clear gap: while many algorithms exist, there is no standardized way to evaluate them under consistent configurations, geometries, and diagnostics. The goal of this project is to design and implement a complete benchmarking suite for VolEsti, enabling systematic, reproducible, and extensible evaluation of geometric random walks. The framework will support configurable experiments, advanced diagnostics, and integration with Python tools for visualization and analysis. Ultimately, we aim to implement a research-grade benchmarking platform where any algorithm can be evaluated quickly and thoroughly and every new suggested algorithm can be easily compared to existing methods.