相关论文: Computing Augustin Information via Hybrid Geodesic…

In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed…

We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in…

In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…

A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…

We propose computationally tractable accelerated first-order methods for Riemannian optimization, extending the Nesterov accelerated gradient (NAG) method. For both geodesically convex and geodesically strongly convex objective functions,…

In this paper, we consider nonlinear optimization problems with nonlinear equality constraints and bound constraints on the variables. For the solution of such problems, many augmented Lagrangian methods have been defined in the literature.…

Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…

We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and H\"older continuous Hessians. The proposed algorithm is a heavy-ball method equipped with two particular restart mechanisms. It…

Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections…

In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form $\alpha/t$. For positive values of $\alpha$,…

We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…

This paper considers distributed optimization problems, where each agent cooperatively minimizes the sum of local objective functions through the communication with its neighbors. The widely adopted distributed gradient method in solving…

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…

In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the…

In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…

In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…

Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…

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…

We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{\L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive…

We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…