相关论文: On Acceleration with Noise-Corrupted Gradients

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…

Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings.…

This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient…

Nesterov's accelerated gradient method (NAG) is widely used in problems with machine learning background including deep learning, and is corresponding to a continuous-time differential equation. From this connection, the property of the…

This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…

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. More precisely, we interpret a large class of…

We introduce a detailed analysis of the convergence of first-order methods with composite noise (sum of relative and absolute) in gradient for convex and smooth function minimization. This paper illustrates instances of practical problems…

Due to the high communication cost in distributed and federated learning problems, methods relying on compression of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods…

Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence…

We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal…

Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process. Distributed and asynchronous variants of gradient descent have been…

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster…

Based on SGD, previous works have proposed many algorithms that have improved convergence speed and generalization in stochastic optimization, such as SGDm, AdaGrad, Adam, etc. However, their convergence analysis under non-convex conditions…

We introduce a framework, which we denote as the augmented estimate sequence, for deriving fast algorithms with provable convergence guarantees. We use this framework to construct a new first-order scheme, the Accelerated Composite Gradient…

In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated…

Nesterov's accelerated gradient methods (AGM) have been successfully applied in many machine learning areas. However, their empirical performance on training max-margin models has been inferior to existing specialized solvers. In this…

Adaptive gradient methods have been widely adopted in training large-scale deep neural networks, especially large foundation models. Despite the huge success in practice, their theoretical advantages over classical gradient methods with…

In this paper, we prove new complexity bounds for zeroth-order methods in non-convex optimization with inexact observations of the objective function values. We use the Gaussian smoothing approach of Nesterov and Spokoiny [2015] and extend…

Gradient Boosting Machine (GBM) is an extremely powerful supervised learning algorithm that is widely used in practice. GBM routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In this…

Accelerated gradient-based methods are being extensively used for solving non-convex machine learning problems, especially when the data points are abundant or the available data is distributed across several agents. Two of the prominent…