Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds

• URL: http://arxiv.org/abs/2406.02296v1
• Date: Tue, 4 Jun 2024 13:17:24 GMT
• Title: Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds
• Authors: Daniel Dodd, Louis Sharrock, Christopher Nemeth,
• Abstract summary: In this work, we introduce innovative learning-rate-free algorithms for optimization over Riemannian. 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.
• Score: 1.6385815610837167
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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