相关论文: Stability and Generalization for Decentralized Mar…

The mini-batch stochastic gradient descent (SGD) algorithm is widely used in training machine learning models, in particular deep learning models. We study SGD dynamics under linear regression and two-layer linear networks, with an easy…

We study a fully decentralized federated learning algorithm, which is a novel gradient descent algorithm executed on a communication-based network. For convenience, we refer to it as a network gradient descent (NGD) method. In the NGD…

Decentralized learning has emerged as a powerful approach for handling large datasets across multiple machines in a communication-efficient manner. However, such methods often face scalability limitations, as increasing the number of…

In this paper, we study the performance of a large family of SGD variants in the smooth nonconvex regime. To this end, we propose a generic and flexible assumption capable of accurate modeling of the second moment of the stochastic…

In this paper we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function…

This manuscript investigates the one-pass stochastic gradient descent (SGD) dynamics of a two-layer neural network trained on Gaussian data and labels generated by a similar, though not necessarily identical, target function. We rigorously…

Mini-batch stochastic gradient methods (SGD) are state of the art for distributed training of deep neural networks. Drastic increases in the mini-batch sizes have lead to key efficiency and scalability gains in recent years. However,…

We develop generalization error bounds for stochastic gradient descent (SGD) with label noise in non-convex settings under uniform dissipativity and smoothness conditions. Under a suitable choice of semimetric, we establish a contraction in…

Stochastic momentum methods have been widely adopted in training deep neural networks. However, their theoretical analysis of convergence of the training objective and the generalization error for prediction is still under-explored. This…

This paper develops algorithms for decentralized machine learning over a network, where data are distributed, computation is localized, and communication is restricted between neighbors. A line of recent research in this area focuses on…

We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…

We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/over-parameterized regime. In this work, we derive precise non-asymptotic error bounds of RF…

Gradient descent (GD) and stochastic gradient descent (SGD) are the workhorses of large-scale machine learning. While classical theory focused on analyzing the performance of these methods in convex optimization problems, the most notable…

Decentralized optimization is emerging as a viable alternative for scalable distributed machine learning, but also introduces new challenges in terms of synchronization costs. To this end, several communication-reduction techniques, such as…

The convergence behavior of Stochastic Gradient Descent (SGD) crucially depends on the stepsize configuration. When using a constant stepsize, the SGD iterates form a Markov chain, enjoying fast convergence during the initial transient…

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear…

It has been experimentally observed that distributed implementations of mini-batch stochastic gradient descent (SGD) algorithms exhibit speedup saturation and decaying generalization ability beyond a particular batch-size. In this work, we…

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation…

Stochastic gradient descent (SGD) is a key ingredient in the training of deep neural networks and yet its geometrical significance appears elusive. We study a deterministic model in which the trajectories of our dynamical systems are…