Related papers: Sign Operator for Coping with Heavy-Tailed Noise i…
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.…
Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…
We study convergence in high-probability of SGD-type methods in non-convex optimization and the presence of heavy-tailed noise. To combat the heavy-tailed noise, a general black-box nonlinear framework is considered, subsuming…
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…
We consider stochastic optimization problems with heavy-tailed noise with structured density. For such problems, we show that it is possible to get faster rates of convergence than $\mathcal{O}(K^{-2(\alpha - 1)/\alpha})$, when the…
Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…
In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability…
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…
In this paper, we present enhanced analysis for sign-based optimization algorithms with momentum updates. Traditional sign-based methods, under the separable smoothness assumption, guarantee a convergence rate of $\mathcal{O}(T^{-1/4})$,…
During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…
While the convergence behaviors of stochastic gradient methods are well understood \emph{in expectation}, there still exist many gaps in the understanding of their convergence with \emph{high probability}, where the convergence rate has a…
We study high-probability convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. In the proposed scenario, the model is updated in an online fashion, as new information is observed, without storing any…
Stochastic Gradient Descent (SGD) is a cornerstone of large-scale optimization, yet its theoretical behavior under heavy-tailed noise -- common in modern machine learning and reinforcement learning -- remains poorly understood. In this…
Stochastic first-order methods such as Stochastic Extragradient (SEG) or Stochastic Gradient Descent-Ascent (SGDA) for solving smooth minimax problems and, more generally, variational inequality problems (VIP) have been gaining a lot of…
Recently, the study of heavy-tailed noises in first-order nonconvex stochastic optimization has gotten a lot of attention since it was recognized as a more realistic condition as suggested by many empirical observations. Specifically, the…
This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased…
We study stochastic nonconvex optimization under heavy-tailed noise. In this setting, the stochastic gradients only have bounded $p$-th central moment ($p$-BCM) for some $p \in (1,2]$. Building on the foundational work of Arjevani et al.…
In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…
While adaptive gradient methods are the workhorse of modern machine learning, sign-based optimization algorithms such as Lion and Muon have recently demonstrated superior empirical performance over AdamW in training large language models…
Randomized subspace methods reduce per-iteration cost; however, in nonconvex optimization, most analyses are expectation-based, and high-probability bounds remain scarce even under sub-Gaussian noise. We first prove that randomized subspace…