相关论文: (S)GD over Diagonal Linear Networks: Implicit Regu…

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two…

Stochastic gradient descent (SGD) is a promising numerical method for solving large-scale inverse problems. However, its theoretical properties remain largely underexplored in the lens of classical regularization theory. In this note, we…

We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the…

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

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…

Stochastic gradient descent (SGD) is the workhorse of large-scale learning, yet classical analyses rely on assumptions that can be either too strong (bounded variance) or too coarse (uniform noise). The expected smoothness (ES) condition…

We study the generalization properties of stochastic gradient methods for learning with convex loss functions and linearly parameterized functions. We show that, in the absence of penalizations or constraints, the stability and…

This paper proposes a thorough theoretical analysis of Stochastic Gradient Descent (SGD) with non-increasing step sizes. First, we show that the recursion defining SGD can be provably approximated by solutions of a time inhomogeneous…

Understanding the dynamics of optimization in deep learning is increasingly important as models scale. While stochastic gradient descent (SGD) and its variants reliably find solutions that generalize well, the mechanisms driving this…

Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…

Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization schemes are frequently employed in applications involving…

Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…

Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theoretical analyses of stochastic gradient algorithms. In this…

We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for…

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…

Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts…

Distributed stochastic gradient descent (SGD) algorithms are widely deployed in training large-scale deep learning models, while the communication overhead among workers becomes the new system bottleneck. Recently proposed gradient…

Both Dimensionality Reduction (DR) and Graph Drawing (GD) aim to visualize abstract, non-linear structures, yet rely on different optimization paradigms. This contrast is evident in Multidimensional Scaling (MDS), which typically depends on…

The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for…

Neural networks typically generalize well when fitting the data perfectly, even though they are heavily overparameterized. Many factors have been pointed out as the reason for this phenomenon, including an implicit bias of stochastic…