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Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones.…

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

Most existing decentralized learning methods with differential privacy (DP) guarantee rely on constant gradient clipping bounds and fixed-level DP Gaussian noises for each node throughout the training process, leading to a significant…

Motivated by understanding and analysis of large-scale machine learning under heavy-tailed gradient noise, we study decentralized optimization with gradient clipping, i.e., in which certain clipping operators are applied to the gradients or…

We study scalable alternatives to robust gradient descent (RGD) techniques that can be used when the losses and/or gradients can be heavy-tailed, though this will be unknown to the learner. The core technique is simple: instead of trying to…

Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these…

We devise a distributed asynchronous stochastic epsilon-gradient-based algorithm to enable a network of computing and communicating nodes to solve a constrained discrete-time time-varying stochastic convex optimization problem. Each node…

Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging…

We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save…

We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized,…

The tension between data privacy and model utility has become the defining bottleneck for the practical deployment of large language models (LLMs) trained on sensitive corpora including healthcare. Differentially private stochastic gradient…

Differentially private (DP) training preserves the data privacy usually at the cost of slower convergence (and thus lower accuracy), as well as more severe mis-calibration than its non-private counterpart. To analyze the convergence of DP…

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…

Prior work on differential privacy analysis of randomized SGD algorithms relies on composition theorems, where the implicit (unrealistic) assumption is that the internal state of the iterative algorithm is revealed to the adversary. As a…

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…

We propose a Stochastic Gradient Descent (SGD)-type algorithm for Personalized Federated Learning which can be particularly attractive for mobile energy-limited regimes due to its low per-client computational cost. The model to be trained…

Heavy-tailed noise in nonconvex stochastic optimization has garnered increasing research interest, as empirical studies, including those on training attention models, suggest it is a more realistic gradient noise condition. This paper…

The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…

Differentially private stochastic gradient descent (DP-SGD) enables private deep learning through per-example clipping and calibrated Gaussian noise, but its high-variance updates can reduce utility on challenging datasets. We propose…

In this paper, we propose a differentially private decentralized learning method (termed PrivSGP-VR) which employs stochastic gradient push with variance reduction and guarantees $(\epsilon, \delta)$-differential privacy (DP) for each node.…