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Stochastic gradient descent (SGD) for strongly convex functions converges at the rate $\bO(1/k)$. However, achieving good results in practice requires tuning the parameters (for example the learning rate) of the algorithm. In this paper we…

Optimization and Control · Mathematics 2019-07-15 Adam M. Oberman , Mariana Prazeres

We propose an adaptive step-size rule for decentralized optimization. Choosing a step-size that balances convergence and stability is challenging. This is amplified in the decentralized setting as agents observe only local (possibly…

Optimization and Control · Mathematics 2026-02-17 Aaron Fainman , Stefan Vlaski

We extend the convergence analysis of AdaSLS and AdaSPS in [Jiang and Stich, 2024] to the nonconvex setting, presenting a unified convergence analysis of stochastic gradient descent with adaptive Armijo line-search (AdaSLS) and Polyak…

Optimization and Control · Mathematics 2025-12-02 Haotian Wu

Machine learning practitioners invest significant manual and computational resources in finding suitable learning rates for optimization algorithms. We provide a probabilistic motivation, in terms of Gaussian inference, for popular…

Machine Learning · Computer Science 2021-02-23 Filip de Roos , Carl Jidling , Adrian Wills , Thomas Schön , Philipp Hennig

We investigate the convergence of stochastic mirror descent (SMD) under interpolation in relatively smooth and smooth convex optimization. In relatively smooth convex optimization we provide new convergence guarantees for SMD with a…

Optimization and Control · Mathematics 2023-05-26 Ryan D'Orazio , Nicolas Loizou , Issam Laradji , Ioannis Mitliagkas

As a foundational architecture of artificial intelligence models, Transformer has been recently adapted to spiking neural networks with promising performance across various tasks. However, existing spiking Transformer(ST)-based models…

Machine Learning · Computer Science 2026-01-06 Hongze Sun , Wuque Cai , Duo Chen , Quan Tang , Shifeng Mao , Jiayi He , Zhenxing Wang , Yan Cui , Dezhong Yao , Daqing Guo

We consider $d$-dimensional linear stochastic approximation algorithms (LSAs) with a constant step-size and the so called Polyak-Ruppert (PR) averaging of iterates. LSAs are widely applied in machine learning and reinforcement learning…

Machine Learning · Computer Science 2017-09-14 Chandrashekar Lakshminarayanan , Csaba Szepesvári

The training of deep neural networks is inherently a nonconvex optimization problem, yet standard approaches such as stochastic gradient descent (SGD) require simultaneous updates to all parameters, often leading to unstable convergence and…

Machine Learning · Computer Science 2025-08-07 Chengcheng Yan , Jiawei Xu , Zheng Peng , Qingsong Wang

Recently the "SP" (Stochastic Polyak step size) method has emerged as a competitive adaptive method for setting the step sizes of SGD. SP can be interpreted as a method specialized to interpolated models, since it solves the interpolation…

Machine Learning · Computer Science 2022-07-19 Shuang Li , William J. Swartworth , Martin Takáč , Deanna Needell , Robert M. Gower

Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for…

Machine Learning · Statistics 2021-06-11 Xiaoyu Li , Zhenxun Zhuang , Francesco Orabona

Spiking neural networks have gained significant attention due to their brain-like information processing capabilities. The use of surrogate gradients has made it possible to train spiking neural networks with backpropagation, leading to…

Neural and Evolutionary Computing · Computer Science 2023-05-24 Dongcheng Zhao , Guobin Shen , Yiting Dong , Yang Li , Yi Zeng

We propose and study Sparse Polyak, a variant of Polyak's adaptive step size, designed to solve high-dimensional statistical estimation problems where the problem dimension is allowed to grow much faster than the sample size. In such…

Optimization and Control · Mathematics 2025-10-16 Tianqi Qiao , Marie Maros

Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…

Machine Learning · Computer Science 2021-03-30 Loris Nanni , Gianluca Maguolo , Alessandra Lumini

Gradient descent is slow to converge for ill-conditioned problems and non-convex problems. An important technique for acceleration is step-size adaptation. The first part of this paper contains a detailed review of step-size adaptation…

Machine Learning · Computer Science 2022-05-27 Hengshuai Yao

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate…

Machine Learning · Computer Science 2019-12-04 Michael R. Zhang , James Lucas , Geoffrey Hinton , Jimmy Ba

Stagewise training strategy is widely used for learning neural networks, which runs a stochastic algorithm (e.g., SGD) starting with a relatively large step size (aka learning rate) and geometrically decreasing the step size after a number…

Machine Learning · Statistics 2019-02-05 Zhuoning Yuan , Yan Yan , Rong Jin , Tianbao Yang

We develop a high-dimensional scaling limit for Stochastic Gradient Descent with Polyak Momentum (SGD-M) and adaptive step-sizes. This provides a framework to rigourously compare online SGD with some of its popular variants. We show that…

Machine Learning · Statistics 2026-02-19 Aukosh Jagannath , Taj Jones-McCormick , Varnan Sarangian

We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method, describes how the performance degrades as the step size…

Optimization and Control · Mathematics 2026-05-27 Fabian Schaipp , Robert M. Gower , Adrien Taylor

Tail Averaging improves on Polyak averaging's non-asymptotic behaviour by excluding a number of leading iterates of stochastic optimization from its calculations. In practice, with a finite number of optimization steps and a learning rate…

Machine Learning · Statistics 2023-04-18 Gábor Melis

Stochastic gradient methods are among the most widely used algorithms for large-scale optimization and machine learning. A key technique for improving the statistical efficiency and stability of these methods is the use of averaging schemes…

Optimization and Control · Mathematics 2026-03-11 K. Lakshmanan