Rieoptax: Riemannian Optimization in JAX

TL;DR

Rieoptax is an open source Python library that enables efficient Riemannian optimization in JAX, supporting various algorithms and differentially private methods, with faster geometric primitives than existing frameworks.

Contribution

The paper introduces Rieoptax, a new library that offers faster Riemannian geometric primitives and supports advanced stochastic and private optimization methods in JAX.

Findings

Faster computation of Riemannian exponential and logarithm maps in Rieoptax.

Supports a wide range of stochastic optimization algorithms.

Includes differentially private Riemannian optimization.

Abstract

We present Rieoptax, an open source Python library for Riemannian optimization in JAX. We show that many differential geometric primitives, such as Riemannian exponential and logarithm maps, are usually faster in Rieoptax than existing frameworks in Python, both on CPU and GPU. We support various range of basic and advanced stochastic optimization solvers like Riemannian stochastic gradient, stochastic variance reduction, and adaptive gradient methods. A distinguishing feature of the proposed toolbox is that we also support differentially private optimization on Riemannian manifolds.