Related papers: Avoiding Bias in Clipped SGD for Overparameterized…

Gradient clipping is a widely used technique in Machine Learning and Deep Learning (DL), known for its effectiveness in mitigating the impact of heavy-tailed noise, which frequently arises in the training of large language models.…

Recent empirical evidence indicates that many machine learning applications involve heavy-tailed gradient noise, which challenges the standard assumptions of bounded variance in stochastic optimization. Gradient clipping has emerged as a…

Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD)…

Traditional analyses in non-convex optimization typically rely on the smoothness assumption, namely requiring the gradients to be Lipschitz. However, recent evidence shows that this smoothness condition does not capture the properties of…

We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called $(L_0,L_1)$-smoothness. Using gradient clipping, we establish a high probability convergence rate that…

There is an increasing realization that algorithmic inductive biases are central in preventing overfitting; empirically, we often see a benign overfitting phenomenon in overparameterized settings for natural learning algorithms, such as…

Stochastic gradient algorithms are often unstable when applied to functions that do not have Lipschitz-continuous and/or bounded gradients. Gradient clipping is a simple and effective technique to stabilize the training process for problems…

The success of modern machine learning is due in part to the adaptive optimization methods that have been developed to deal with the difficulties of training large models over complex datasets. One such method is gradient clipping: a…

Due to the non-smoothness of optimization problems in Machine Learning, generalized smoothness assumptions have been gaining a lot of attention in recent years. One of the most popular assumptions of this type is $(L_0,L_1)$-smoothness…

Gradient clipping is a standard safeguard for training neural networks under noisy, heavy-tailed stochastic gradients; yet, most clipping rules treat all parameters as vectors and ignore the matrix structure of modern architectures. We show…

This paper studies the convergence of clipped stochastic gradient descent (SGD) algorithms with decision-dependent data distribution. Our setting is motivated by privacy preserving optimization algorithms that interact with performative…

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…

We develop a worst-case complexity theory for stochastically preconditioned stochastic gradient descent (SPSGD) and its accelerated variants under heavy-tailed noise, a setting that encompasses widely used adaptive methods such as Adam,…

Gradient clipping has long been considered essential for ensuring the convergence of Stochastic Gradient Descent (SGD) in the presence of heavy-tailed gradient noise. In this paper, we revisit this belief and explore whether gradient…

Most modern learning problems are highly overparameterized, meaning that there are many more parameters than the number of training data points, and as a result, the training loss may have infinitely many global minima (parameter vectors…

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning…

Optimization under heavy-tailed noise has become popular recently, since it better fits many modern machine learning tasks, as captured by empirical observations. Concretely, instead of a finite second moment on gradient noise, a bounded…

It is often observed that stochastic gradient descent (SGD) and its variants implicitly select a solution with good generalization performance; such implicit bias is often characterized in terms of the sharpness of the minima. Kleinberg et…

$L_0$-smoothness, which has been pivotal to advancing decentralized optimization theory, is often fairly restrictive for modern tasks like deep learning. The recent advent of relaxed $(L_0,L_1)$-smoothness condition enables improved…

Gradient clipping is a standard training technique used in deep learning applications such as large-scale language modeling to mitigate exploding gradients. Recent experimental studies have demonstrated a fairly special behavior in the…