Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds

Dodd, Daniel and Sharrock, Louis and Nemeth, Christopher (2024) Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds. Proceedings of Machine Learning Research. ISSN 1938-7228 (In Press)

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Abstract

In recent years, interest in gradient-based optimization over Riemannian manifolds has surged. However, a significant challenge lies in the reliance on hyperparameters, especially the learning rate, which requires meticulous tuning by practitioners to ensure convergence at a suitable rate. In this work, we introduce innovative learning- rate-free algorithms for stochastic optimization over Riemannian manifolds, eliminating the need for hand-tuning and providing a more robust and user-friendly approach. We establish high probability convergence guarantees that are optimal, up to logarithmic factors, compared to the best-known optimally tuned rate in the deterministic setting. Our approach is validated through numerical experiments, demonstrating competitive performance against learning-rate-dependent algorithms.