# Implicit Riemannian Optimism with Applications to Min-Max Problems

arXiv: https://arxiv.org/abs/2501.18381 · HTML: https://mlsanity.com/paper/2501.18381/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2025.

## Built on by (most cited first, 4 of 4)

- [Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives](https://mlsanity.com/paper/2509.11236/) (2025)
- [Distribution-informed Online Conformal Prediction](https://mlsanity.com/paper/2512.07770/) (2025)
- [Curvature-Independent Regret Bounds for Distributed Online Optimization on Hadamard Manifolds](https://mlsanity.com/paper/2609.13646/) (2026)
- [Retraction-Based Gradient Projection Algorithms on Manifolds](https://mlsanity.com/paper/2609.30885/) (2026)

## Abstract (arXiv)

We introduce a Riemannian optimistic online learning algorithm for Hadamard manifolds based on inexact implicit updates. Unlike prior work, our method can handle in-manifold constraints, and matches the best known regret bounds in the Euclidean setting with no dependence on geometric constants, like the minimum curvature. Building on this, we develop algorithms for g-convex, g-concave smooth min-max problems on Hadamard manifolds. Notably, one method nearly matches the gradient oracle complexity of the lower bound for Euclidean problems, for the first time.