New Riemannian optimization algorithm extends to positive curvature manifolds

Researchers have developed a new decentralized online Riemannian optimization algorithm capable of operating beyond the limitations of Hadamard manifolds, extending its applicability to spaces with positive curvature. The algorithm incorporates a curvature-aware consensus step that facilitates linear convergence even in these more complex geometric settings. This advancement leads to a $O(\sqrt{T})$ regret bound for the decentralized online Riemannian gradient descent method, with similar bounds achieved in a two-point bandit feedback scenario using efficient gradient estimators. AI

RANK_REASON This is a research paper published on arXiv detailing a new optimization algorithm. [lever_c_demoted from research: ic=1 ai=1.0]

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• Emre Sahinoglu

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