Related papers: Generalization Guarantees on Data-Driven Tuning of…

Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several…

We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…

Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a…

Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of…

Most prior work on the convergence of gradient descent (GD) for overparameterized neural networks relies on strong assumptions on the step size (infinitesimal), the hidden-layer width (infinite), or the initialization (large, spectral,…

Fractional Gradient Descent (FGD) offers a novel and promising way to accelerate optimization by incorporating fractional calculus into machine learning. Although FGD has shown encouraging initial results across various optimization tasks,…

Stochastic Gradient Descent (SGD) is a central tool in machine learning. We prove that SGD converges to zero loss, even with a fixed (non-vanishing) learning rate - in the special case of homogeneous linear classifiers with smooth monotone…

We analyze the sample complexity of full-batch Gradient Descent (GD) in the setup of non-smooth Stochastic Convex Optimization. We show that the generalization error of GD, with common choice of hyper-parameters, can be $\tilde \Theta(d/m +…

Tuning hyperparameters, such as the stepsize, presents a major challenge of training machine learning models. To address this challenge, numerous adaptive optimization algorithms have been developed that achieve near-optimal complexities,…

Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…

The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values…

Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…

Overparametrized neural networks trained by gradient descent (GD) can provably overfit any training data. However, the generalization guarantee may not hold for noisy data. From a nonparametric perspective, this paper studies how well…

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…

One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies…

The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…

Machine unlearning has raised significant interest with the adoption of laws ensuring the ``right to be forgotten''. Researchers have provided a probabilistic notion of approximate unlearning under a similar definition of Differential…

A convolutional neural network (ConvNet) is usually trained and then tested using images drawn from the same distribution. To generalize a ConvNet to various tasks often requires a complete training dataset that consists of images drawn…

We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer neural network with random iid inputs. We study the generalization performances of standard classifiers in the…

Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a global optimizer with perfect fit (zero-loss) in many…