Related papers: Accelerated Flow for Probability Distributions
We consider problems of minimizing functionals $\mathcal{F}$ of probability measures on the Euclidean space. To propose an accelerated gradient descent algorithm for such problems, we consider gradient flow of transport maps that give…
The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While much attention has been directed towards optimizing within…
Various distributed gradient descent algorithms for multi-agent optimization have incorporated the Nesterov accelerated gradient method, where the use of momentum enhances convergence rates. These algorithms have found broad applications in…
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…
Nesterov's accelerated gradient algorithm is derived from first principles. The first principles are founded on the recently-developed optimal control theory for optimization. This theory frames an optimization problem as an optimal control…
We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically…
A novel dynamical inertial Newton system, which is called Hessian-driven Nesterov accelerated gradient (H-NAG) flow is proposed. Convergence of the continuous trajectory are established via tailored Lyapunov function, and new first-order…
We propose a class of discrete state sampling algorithms based on Nesterov's accelerated gradient method, which extends the classical Metropolis-Hastings (MH) algorithm. The evolution of the discrete states probability distribution governed…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
We develop a theory of accelerated first-order optimization from the viewpoint of differential equations and Lyapunov functions. Building upon the previous work of many researchers, we consider differential equations which model the…
We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov…
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…
We consider a distributed stochastic optimization problem that is solved by a decentralized network of agents with only local communication between neighboring agents. The goal of the whole system is to minimize a global objective function…
This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalised by the relative entropy. We identify suitable metric space on which we construct a gradient flow for the…
The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest…
We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…
The search for equilibrium in a two-stage traffic flow model reduces to the solution of a special nonsmooth convex optimization problem with two groups of different variables. For numerical solution of this problem, the paper proposes to…
This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density,…
This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…
We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gradient-flow dynamics via the Weighted-Energy-Dissipation…