Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation

TL;DR

Pymanopt is a Python toolbox that simplifies optimization on manifolds by integrating automatic differentiation, making advanced geometric optimization techniques more accessible and easier to implement.

Contribution

It introduces a Python-based toolbox that combines manifold geometries, optimization algorithms, and automatic differentiation to ease experimentation with manifold optimization.

Findings

Automates derivative calculations using automatic differentiation.

Provides manifold geometries and optimization algorithms in Python.

Reduces implementation errors and development time.

Abstract

Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable manifold. While many optimization problems are of the described form, technicalities of differential geometry and the laborious calculation of derivatives pose a significant barrier for experimenting with these methods. We introduce Pymanopt (available at https://pymanopt.github.io), a toolbox for optimization on manifolds, implemented in Python, that---similarly to the Manopt Matlab toolbox---implements several manifold geometries and optimization algorithms. Moreover, we lower the barriers to users further by using automated differentiation for calculating derivative information, saving users time and saving them from potential calculation and implementation errors.