相关论文: Nesterov Acceleration for Ensemble Kalman Inversio…

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. This point of view covers the stochastic gradient…

The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…

The proximal point method (PPM) is a fundamental method in optimization that is often used as a building block for designing optimization algorithms. In this work, we use the PPM method to provide conceptually simple derivations along with…

The extrapolation strategy raised by Nesterov, which can accelerate the convergence rate of gradient descent methods by orders of magnitude when dealing with smooth convex objective, has led to tremendous success in training machine…

Nesterov's accelerated gradient method for minimizing a smooth strongly convex function $f$ is known to reduce $f(\x_k)-f(\x^*)$ by a factor of $\eps\in(0,1)$ after $k\ge O(\sqrt{L/\ell}\log(1/\eps))$ iterations, where $\ell,L$ are the two…

We show that the mean-field underdamped Langevin process (associated to the non-linear Vlasov-Fokker-Planck equation) achieves a Nesterov acceleration with respect to the Wasserstein gradient flow of a displacement-convex free energy, in…

Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. While many generalizations and extensions of Nesterov's original acceleration method have been proposed, it is not yet clear what is…

Gradient compression is a recent and increasingly popular technique for reducing the communication cost in distributed training of large-scale machine learning models. In this work we focus on developing efficient distributed methods that…

We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective…

In convex optimization, there is an {\em acceleration} phenomenon in which we can boost the convergence rate of certain gradient-based algorithms. We can observe this phenomenon in Nesterov's accelerated gradient descent, accelerated mirror…

While momentum-based optimization algorithms are commonly used in the notoriously non-convex optimization problems of deep learning, their analysis has historically been restricted to the convex and strongly convex setting. In this article,…

In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $\mu_F$- and $\mu_G$-strongly convex functions, respectively. By incorporating Nesterov…

Black-box variational inference (BBVI) with Gaussian mixture families offers a flexible approach for approximating complex posterior distributions without requiring gradients of the target density. However, standard numerical optimization…

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by…

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…

This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a…

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

Stochastic optimization is a vital field in the realm of mathematical optimization, finding applications in diverse areas ranging from operations research to machine learning. In this paper, we introduce a novel first-order optimization…

Transmission electron microscopes (TEMs) enable atomic-scale imaging but suffer from aberrations caused by lens imperfections and environmental conditions, reducing image quality. These aberrations can be compensated by adjusting…

We present and analyze a momentum-based gradient method for training linear classifiers with an exponentially-tailed loss (e.g., the exponential or logistic loss), which maximizes the classification margin on separable data at a rate of…