Rieoptax: Riemannian Optimization in JAX
This is an incremental contribution providing a new library for researchers and practitioners in machine learning and optimization, with added support for differentially private optimization on manifolds.
The authors introduced Rieoptax, an open-source Python library for Riemannian optimization in JAX, demonstrating that it often provides faster performance for geometric primitives like exponential and logarithm maps compared to existing frameworks on CPU and GPU.
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.