Related papers: Differential Evolution for Grassmann Manifold Opti…

We give curvature-dependant convergence rates for the optimization of weakly convex functions defined on a manifold of 1-bounded geometry via Riemannian gradient descent and via the dynamic trivialization algorithm. In order to do this, we…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…

In this paper, we extend a recently established subgradient method for the computation of Riemannian metrics that optimizes certain singular value functions associated with dynamical systems. This extension is threefold. First, we introduce…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

In this paper, We propose a general Riemannian proximal optimization algorithm with guaranteed convergence to solve Markov decision process (MDP) problems. To model policy functions in MDP, we employ Gaussian mixture model (GMM) and…

Over the past twenty years, artificial Gene Regulatory Networks (GRNs) have shown their capacity to solve real-world problems in various domains such as agent control, signal processing and artificial life experiments. They have also…

This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel…

It has been observed in a variety of contexts that gradient descent methods have great success in solving low-rank matrix factorization problems, despite the relevant problem formulation being non-convex. We tackle a particular instance of…

In recent years, Riemannian stochastic gradient descent (R-SGD), Riemannian stochastic variance reduction (R-SVRG) and Riemannian stochastic recursive gradient (R-SRG) have attracted considerable attention on Riemannian optimization. Under…

Local-gradient-based optimization approaches lack nonlocal exploration ability required for escaping from local minima in non-convex landscapes. A directional Gaussian smoothing (DGS) approach was recently proposed by the authors (Zhang et…

This paper investigates the optimal $H_2$ model order reduction for linear systems with quadratic outputs. In the framework of Galerkin projection, we first formulate the optimal $H_2$ MOR as an unconstrained Riemannian optimization problem…

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…

The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product…

In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

We propose a computationally efficient algorithm for gradient-based linear dimension reduction and high-dimensional regression. The algorithm initially computes a Mondrian forest and uses this estimator to identify a relevant feature…

Strictly enforcing orthonormality constraints on parameter matrices has been shown advantageous in deep learning. This amounts to Riemannian optimization on the Stiefel manifold, which, however, is computationally expensive. To address this…