相关论文: On the Convergence of Nesterov's Accelerated Gradi…
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with…
This paper considers the problem of understanding the behavior of a general class of accelerated gradient methods on smooth nonconvex functions. Motivated by some recent works that have proposed effective algorithms, based on Polyak's heavy…
The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss…
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,…
Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…
We develop an adaptive Nesterov accelerated proximal gradient (adaNAPG) algorithm for stochastic composite optimization problems, boosting the Nesterov accelerated proximal gradient (NAPG) algorithm through the integration of an adaptive…
We present a dynamical system framework for understanding Nesterov's accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from…
We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show…
We present a coupled system of ODEs which, when discretized with a constant time step/learning rate, recovers Nesterov's accelerated gradient descent algorithm. The same ODEs, when discretized with a decreasing learning rate, leads to novel…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
Momentum based stochastic gradient methods such as heavy ball (HB) and Nesterov's accelerated gradient descent (NAG) method are widely used in practice for training deep networks and other supervised learning models, as they often provide…
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…
We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…
We present a generalization of Nesterov's accelerated gradient descent algorithm. Our algorithm (AGNES) provably achieves acceleration for smooth convex and strongly convex minimization tasks with noisy gradient estimates if the noise…
Nesterov's accelerated gradient descent method (AGD) is a seminal deterministic first-order method known to achieve the optimal order of iteration complexity for solving convex smooth optimization problems. Two distinct sequences of…
We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness of our method, we perform numerical experiments which demonstrate that…
We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical…
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…
We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…
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…