No-regret Online Learning over Riemannian Manifolds
Dec 6, 2021
Speakers
Zhipeng Tu
Speaker · 0 followers
Yiguang Hong
Speaker · 0 followers
Guodong Shi
Speaker · 0 followers
About
We consider online optimization over Riemannian manifolds, where a learner attempts to minimize a sequence of time-varying loss functions defined on Riemannian manifolds. Though many Euclidean online convex optimization algorithms have been proven useful in a wide range of areas, less attention has been paid to their Riemannian counterparts. In this paper, we study a Riemannian online gradient descent algorithm (R-OGD) on Hadamard manifolds for both geodesically convex and strongly geodesically convex loss functions, and a Riemannian bandit algorithm (R-BAN) on Hadamard homogeneous manifolds for geodesically convex functions. We establish upper bounds on the regret of the algorithms with respect to time horizon T, manifold curvature κ, and manifold dimension d. We also find a universal lower bound for the achievable regret by an online convex optimization algorithm on Hadamard manifolds. All the obtained regret bounds match the corresponding results in Euclidean spaces. Finally, numerical experiments of the Karcher mean problem validate our theoretical results.We consider online optimization over Riemannian manifolds, where a learner attempts to minimize a sequence of time-varying loss functions defined on Riemannian manifolds. Though many Euclidean online convex optimization algorithms have been proven useful in a wide range of areas, less attention has been paid to their Riemannian counterparts. In this paper, we study a Riemannian online gradient descent algorithm (R-OGD) on Hadamard manifolds for both geodesically convex and strongly geodesically…
Organizer
NeurIPS 2021
Account · 1.9k followers
About NeurIPS 2021
Neural Information Processing Systems (NeurIPS) is a multi-track machine learning and computational neuroscience conference that includes invited talks, demonstrations, symposia and oral and poster presentations of refereed papers. Following the conference, there are workshops which provide a less formal setting.
Like the format? Trust SlidesLive to capture your next event!
Professional recording and live streaming, delivered globally.
Sharing
Recommended Videos
Presentations on similar topic, category or speaker
Actively Identifying Causal Effects with Latent Variables Given Only Response Variable Observable
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Scalable Primitives for Generalized Sensor Fusion (GSF) in Autonomous Vehicles
Watch later
Sammy Sidhu, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Accumulative Poisoning Attacks on Real-time Data
Watch later
Tianyu Pang, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Does Preprocessing Help Training Over-parameterized Neural Networks?
Watch later
Zhao Song, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
BiToD: A Bilingual Multi-Domain Dataset For Task-Oriented Dialogue Modeling
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Addressing Algorithmic Disparity and Performance Inconsistency in Federated Learning
Watch later
Sen Cui, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%