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Implicit Riemannian Optimism with Applications to Min-Max Problems

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arxiv 2501.18381 v1 pith:2DLFDPS2 submitted 2025-01-30 math.OC cs.LG

classification math.OCcs.LG
keywords problemseuclideanhadamardimplicitmanifoldsmatchesmethodmin-max
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms

    math.OC 2025-05 conditional novelty 7.0 of 10

    A new class of functions, horospherically convex functions, admits gradient, subgradient, and accelerated methods with curvature-independent Euclidean rates on Hadamard manifolds.

  2. The Intrinsic Riemannian Proximal Gradient Method for Convex Optimization

    math.OC 2025-07 reject novelty 6.0 of 10

    An intrinsic Riemannian proximal gradient method is shown to converge sublinearly on geodesically convex problems and linearly on strongly convex problems over Hadamard manifolds.

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