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Implicit Riemannian Optimism with Applications to Min-Max Problems
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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
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Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms
A new class of functions, horospherically convex functions, admits gradient, subgradient, and accelerated methods with curvature-independent Euclidean rates on Hadamard manifolds.
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The Intrinsic Riemannian Proximal Gradient Method for Convex Optimization
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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