Related papers: Data-Dependent Stability of Stochastic Gradient De…
This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions.…
We establish generalization error bounds for stochastic gradient Langevin dynamics (SGLD) with constant learning rate under the assumptions of dissipativity and smoothness, a setting that has received increased attention in the…
In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and…
An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…
Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…
Stochastic gradient descent (SGD) is the optimization algorithm of choice in many machine learning applications such as regularized empirical risk minimization and training deep neural networks. The classical convergence analysis of SGD is…
Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of…
We provide novel information-theoretic generalization bounds for stochastic gradient Langevin dynamics (SGLD) under the assumptions of smoothness and dissipativity, which are widely used in sampling and non-convex optimization studies. Our…
Stochastic optimization via Stochastic Gradient Descent (SGD) is a fundamental problem in statistics and optimization. This paper revisits Stochastic Gradient Descent (SGD) for strongly convex objectives, establishing tight, uniform-in-time…
While significant theoretical progress has been achieved, unveiling the generalization mystery of overparameterized neural networks still remains largely elusive. In this paper, we study the generalization behavior of shallow neural…
We consider the generalization error associated with stochastic gradient descent on a smooth convex function over a compact set. We show the first bound on the generalization error that vanishes when the number of iterations $T$ and the…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…
Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…
Information-theoretic generalization bounds analyze stochastic optimization by relating expected generalization error to the mutual information between learned parameters and training data. Virtual perturbation analyses of SGD add auxiliary…
Heavy-tail phenomena in stochastic gradient descent (SGD) have been reported in several empirical studies. Experimental evidence in previous works suggests a strong interplay between the heaviness of the tails and generalization behavior of…
Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…
Stochastic Gradient Descent (SGD) plays a central role in modern machine learning. While there is extensive work on providing error upper bound for SGD, not much is known about SGD error lower bound. In this paper, we study the convergence…
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…
Stability analysis is an essential aspect of studying the generalization ability of deep learning, as it involves deriving generalization bounds for stochastic gradient descent-based training algorithms. Adversarial training is the most…
Many machine learning tasks can be formulated as a stochastic compositional optimization (SCO) problem such as reinforcement learning, AUC maximization, and meta-learning, where the objective function involves a nested composition…