Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds
This work addresses a practical problem for practitioners in machine learning and optimization by providing a more robust and user-friendly approach to stochastic optimization on manifolds, though it is incremental as it builds on existing optimization methods.
The paper tackles the challenge of hyperparameter tuning in gradient-based optimization over Riemannian manifolds by introducing learning-rate-free algorithms, which eliminate the need for hand-tuning and achieve optimal convergence guarantees up to logarithmic factors compared to tuned rates.
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.