Curvature-independent last-iterate convergence for games on riemannian manifolds
Numerous applications in machine learning and data analytics can be formulated as
equilibrium computation over Riemannian manifolds. Despite the extensive investigation of …
equilibrium computation over Riemannian manifolds. Despite the extensive investigation of …
Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles
C Criscitiello, N Boumal - Conference on Learning Theory, 2022 - proceedings.mlr.press
Hamilton and Moitra (2021) showed that, in certain regimes, it is not possible to accelerate
Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms …
Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms …
Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles
C Criscitiello, N Boumal - arXiv preprint arXiv:2111.13263, 2021 - arxiv.org
Hamilton and Moitra (2021) showed that, in certain regimes, it is not possible to accelerate
Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms …
Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms …
Accelerated riemannian optimization: Handling constraints with a prox to bound geometric penalties
D Martínez-Rubio, S Pokutta - The Thirty Sixth Annual …, 2023 - proceedings.mlr.press
We propose a globally-accelerated, first-order method for the optimization of smooth and
(strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We …
(strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We …
Riemannian accelerated gradient methods via extrapolation
In this paper, we propose a convergence acceleration scheme for general Riemannian
optimization problems by extrapolating iterates on manifolds. We show that when the …
optimization problems by extrapolating iterates on manifolds. We show that when the …
Accelerated Bregmann divergence optimization with SMART: an information geometry point of view
M Raus, Y Elshiaty, S Petra - arXiv preprint arXiv:2401.05196, 2024 - arxiv.org
We investigate the problem of minimizing Kullback-Leibler divergence between a linear
model $ Ax $ and a positive vector $ b $ in different convex domains (positive orthant, $ n …
model $ Ax $ and a positive vector $ b $ in different convex domains (positive orthant, $ n …
Riemannian Accelerated Zeroth-order Algorithm: Improved Robustness and Lower Query Complexity
C He, Z Pan, X Wang, B Jiang - arXiv preprint arXiv:2405.05713, 2024 - arxiv.org
Optimization problems with access to only zeroth-order information of the objective function
on Riemannian manifolds arise in various applications, spanning from statistical learning to …
on Riemannian manifolds arise in various applications, spanning from statistical learning to …
Changes from classical statistics to modern statistics and data science
K Zhang, S Liu, M Xiong - arXiv preprint arXiv:2211.03756, 2022 - arxiv.org
A coordinate system is a foundation for every quantitative science, engineering, and
medicine. Classical physics and statistics are based on the Cartesian coordinate system …
medicine. Classical physics and statistics are based on the Cartesian coordinate system …
Decentralized Online Riemannian Optimization with Dynamic Environments
H Chen, Q Sun - arXiv preprint arXiv:2410.05128, 2024 - arxiv.org
This paper develops the first decentralized online Riemannian optimization algorithm on
Hadamard manifolds. Our algorithm, the decentralized projected Riemannian gradient …
Hadamard manifolds. Our algorithm, the decentralized projected Riemannian gradient …
Perspectives on Geometry and Optimization: from Measures to Neural Networks
FS Colmenares - 2023 - search.proquest.com
This thesis explores geometrical aspects of matrix completion, interior point methods,
unbalanced optimal transport, and neural network training. We use these examples to …
unbalanced optimal transport, and neural network training. We use these examples to …