6 papers
Curvature-Independent Regret Bounds for Distributed Online Optimization on Hadamard Manifolds
Zhanyuan Cai, Emre Sahinoglu, Shahin Shahrampour
This work addresses decentralized online Riemannian optimization on Hadamard manifolds. Prior work under geodesic convexity (g-convexity) may require curvature information in the o…
Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions
Zhanyuan Cai, Emre Sahinoglu, Shahin Shahrampour
We study decentralized online optimization for strongly geodesically convex (strongly g-convex) losses on Riemannian manifolds with bounded sectional curvature, including positivel…
Finite-Time Analysis of Stochastic Nonconvex Nonsmooth Optimization on the Riemannian Manifolds
Emre Sahinoglu, Youbang Sun, Shahin Shahrampour
This work addresses the finite-time analysis of nonsmooth nonconvex stochastic optimization under Riemannian manifold constraints. We adapt the notion of Goldstein stationarity to…
Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives
Emre Sahinoglu, Shahin Shahrampour
We study online Riemannian optimization on Hadamard manifolds under the framework of horospherical convexity (h-convexity). Prior work mostly relies on the geodesic convexity (g-co…
Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds
Emre Sahinoglu, Shahin Shahrampour
We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techni…
Online Optimization Perspective on First-Order and Zero-Order Decentralized Nonsmooth Nonconvex Stochastic Optimization
Emre Sahinoglu, Shahin Shahrampour
We investigate the finite-time analysis of finding ()-stationary points for nonsmooth nonconvex objectives in decentralized stochastic optimization. A set of agents aim at min…