Related papers: Momentum Improves Normalized SGD
Large-batch SGD is important for scaling training of deep neural networks. However, without fine-tuning hyperparameter schedules, the generalization of the model may be hampered. We propose to use batch augmentation: replicating instances…
Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient…
This paper introduces a novel approach to enhance the performance of the stochastic gradient descent (SGD) algorithm by incorporating a modified decay step size based on $\frac{1}{\sqrt{t}}$. The proposed step size integrates a logarithmic…
Stochastic Gradient Descent (SGD) is fundamental for training deep neural networks, especially in non-convex settings. Understanding SGD's generalization properties is crucial for ensuring robust model performance on unseen data. In this…
We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…
We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific…
Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and…
We revisit the classical problem of finding an approximately stationary point of the average of $n$ smooth and possibly nonconvex functions. The optimal complexity of stochastic first-order methods in terms of the number of gradient…
SGD with momentum is one of the key components for improving the performance of neural networks. For decentralized learning, a straightforward approach using momentum is Distributed SGD (DSGD) with momentum (DSGDm). However, DSGDm performs…
Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…
Stochastic Gradient Descent (SGD) and its variants are the most used algorithms in machine learning applications. In particular, SGD with adaptive learning rates and momentum is the industry standard to train deep networks. Despite the…
Modern machine learning focuses on highly expressive models that are able to fit or interpolate the data completely, resulting in zero training loss. For such models, we show that the stochastic gradients of common loss functions satisfy a…
Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…
Stochastic heavy ball momentum (SHB) is commonly used to train machine learning models, and often provides empirical improvements over stochastic gradient descent. By primarily focusing on strongly-convex quadratics, we aim to better…
In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…
We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…
The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied…
Momentum is a popular technique to accelerate the convergence in practical training, and its impact on convergence guarantee has been well-studied for first-order algorithms. However, such a successful acceleration technique has not yet…
Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…
We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…