Riemannian Projection-free Online Learning
Authors: Zihao Hu, Guanghui Wang, Jacob D. Abernethy
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we present methods for obtaining sub-linear regret guarantees in online geodesically convex optimization on curved spaces for two scenarios: when we have access to (a) a separation oracle or (b) a linear optimization oracle. For geodesically convex losses, and when a separation oracle is available, our algorithms achieve O(T 1/2), O(T 3/4) and O(T 1/2) adaptive regret guarantees in the full information setting, the bandit setting with one-point feedback and the bandit setting with two-point feedback, respectively. When a linear optimization oracle is available, we obtain regret rates of O(T 3/4) for geodesically convex losses and O(T 2/3 log T) for strongly geodesically convex losses. |
| Researcher Affiliation | Collaboration | Zihao Hu , Guanghui Wang , Jacob Abernethy , College of Computing, Georgia Institute of Technology Google Research |
| Pseudocode | Yes | Algorithm 1: Infeasible Riemannian OGD, Algorithm 2: Infeasible Projection onto (1 δ)K with a Riemannian Separation Oracle, Algorithm 3: Infeasible R-OGD with a separation oracle, Algorithm 4: One-point bandit convex optimization on manifolds with a separation oracle, Algorithm 5: Two-point bandit convex optimization on manifolds with a separation oracle, Algorithm 6: Separating Hyperplane via RFW, Algorithm 7: Closer Infeasible Projection via LOO, Algorithm 8: Block OGD on manifolds with a linear optimization oracle, Algorithm 9: Riemannian Frank-Wolfe with line-search |
| Open Source Code | No | The paper does not provide any links to open-source code or state that the code will be released. |
| Open Datasets | No | The paper is theoretical and does not describe any experimental training on datasets. |
| Dataset Splits | No | The paper is theoretical and does not describe any experimental validation on datasets. |
| Hardware Specification | No | The paper is theoretical and does not mention any hardware specifications used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not list specific software dependencies with version numbers for experimental setup. |
| Experiment Setup | No | The paper is theoretical and does not provide an experimental setup section with hyperparameters or training configurations. |