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Many machine learning models require a training procedure based on running stochastic gradient descent. A key element for the efficiency of those algorithms is the choice of the learning rate schedule. While finding good learning rates…

Machine Learning · Statistics 2020-06-26 Victor Picheny , Vincent Dutordoir , Artem Artemev , Nicolas Durrande

We study adaptive learning rate scheduling for norm-constrained optimizers (e.g., Muon and Lion). We introduce a generalized smoothness assumption under which local curvature decreases with the suboptimality gap and empirically verify that…

Machine Learning · Computer Science 2026-05-19 Artem Riabinin , Andrey Veprikov , Arman Bolatov , Martin Takáč , Aleksandr Beznosikov

Optimizing deep neural networks is largely thought to be an empirical process, requiring manual tuning of several hyper-parameters, such as learning rate, weight decay, and dropout rate. Arguably, the learning rate is the most important of…

Machine Learning · Computer Science 2020-08-04 Rahul Yedida , Snehanshu Saha , Tejas Prashanth

Learning rate schedules are ubiquitously used to speed up and improve optimisation. Many different policies have been introduced on an empirical basis, and theoretical analyses have been developed for convex settings. However, in many…

Machine Learning · Computer Science 2022-02-10 Stéphane d'Ascoli , Maria Refinetti , Giulio Biroli

With the emergence of distributed data, training machine learning models in the serverless manner has attracted increasing attention in recent years. Numerous training approaches have been proposed in this regime, such as decentralized SGD.…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-08-25 Hongchang Gao , Heng Huang

We study the problem of optimizing Large Language Model (LLM) inference scheduling to minimize total latency. LLM inference is an online and multi-task service process and also heavily energy consuming by which a pre-trained LLM processes…

Machine Learning · Computer Science 2025-09-03 Zixi Chen , Yinyu Ye , Zijie Zhou

The ever-growing availability of unlabeled data presents both opportunities and challenges for training artificial intelligence systems. While self-supervised learning (SSL) has emerged as a powerful paradigm for extracting meaningful…

Machine Learning · Computer Science 2025-09-11 Vaibhav Singh , Paul Janson , Paria Mehrbod , Adam Ibrahim , Irina Rish , Eugene Belilovsky , Benjamin Thérien

Learning rate scheduling plays a critical role in the optimization of deep neural networks, directly influencing convergence speed, stability, and generalization. While existing schedulers such as cosine annealing, cyclical learning rates,…

Machine Learning · Computer Science 2026-03-05 Ayush K. Varshney , Šarūnas Girdzijauskas , Konstantinos Vandikas , Aneta Vulgarakis Feljan

The learning rate is a crucial hyperparameter in deep learning, with its ideal value depending on the problem and potentially changing during training. In this paper, we investigate the practical utility of adaptive learning rate mechanisms…

Machine Learning · Computer Science 2025-08-08 Asma Atamna , Tom Maus , Fabian Kievelitz , Tobias Glasmachers

We propose a new per-layer adaptive step-size procedure for stochastic first-order optimization methods for minimizing empirical loss functions in deep learning, eliminating the need for the user to tune the learning rate (LR). The proposed…

Machine Learning · Computer Science 2023-07-07 Achraf Bahamou , Donald Goldfarb

Learning how to learn efficiently is a fundamental challenge for biological agents and a growing concern for artificial ones. To learn effectively, an agent must regulate its learning speed, balancing the benefits of rapid improvement…

Machine Learning · Computer Science 2026-01-13 Valentina Njaradi , Rodrigo Carrasco-Davis , Peter E. Latham , Andrew Saxe

In most practical settings and theoretical analyses, one assumes that a model can be trained until convergence. However, the growing complexity of machine learning datasets and models may violate such assumptions. Indeed, current approaches…

Computer Vision and Pattern Recognition · Computer Science 2020-07-01 Mengtian Li , Ersin Yumer , Deva Ramanan

The learning rate (LR) is one of the most important hyper-parameters in stochastic gradient descent (SGD) algorithm for training deep neural networks (DNN). However, current hand-designed LR schedules need to manually pre-specify a fixed…

Machine Learning · Computer Science 2021-05-14 Jun Shu , Yanwen Zhu , Qian Zhao , Zongben Xu , Deyu Meng

Asynchronous stochastic gradient descent (SGD) enables scalable distributed training but suffers from gradient staleness. Existing mitigation strategies, such as delay-adaptive learning rates and staleness-aware filtering, typically…

Machine Learning · Computer Science 2026-05-15 Tehila Dahan , Roie Reshef , Sharon Goldstein , Kfir Y. Levy

Momentum is a widely used technique for gradient-based optimizers in deep learning. In this paper, we propose a decaying momentum (\textsc{Demon}) rule. We conduct the first large-scale empirical analysis of momentum decay methods for…

Machine Learning · Computer Science 2021-07-02 John Chen , Cameron Wolfe , Zhao Li , Anastasios Kyrillidis

It is known that the standard stochastic gradient descent (SGD) optimization method, as well as accelerated and adaptive SGD optimization methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (as,…

Optimization and Control · Mathematics 2024-06-21 Steffen Dereich , Arnulf Jentzen , Adrian Riekert

We propose an algorithm for the adaptation of the learning rate for stochastic gradient descent (SGD) that avoids the need for validation set use. The idea for the adaptiveness comes from the technique of extrapolation: to get an estimate…

Machine Learning · Statistics 2020-08-28 Antti Koskela , Antti Honkela

Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when…

Computational Finance · Quantitative Finance 2019-09-24 Nikolaos Passalis , Anastasios Tefas , Juho Kanniainen , Moncef Gabbouj , Alexandros Iosifidis

The performance of an optimizer on large-scale deep learning models depends critically on fine-tuning the learning rate, often requiring an extensive grid search over base learning rates, schedules, and other hyperparameters. In this paper,…

Machine Learning · Computer Science 2025-06-11 Ruichen Jiang , Ali Kavis , Aryan Mokhtari

We analyze the convergence behavior of stochastic gradient descent with momentum (SGDM) under dynamic learning-rate and batch-size schedules by introducing a novel and simpler Lyapunov function. We extend the existing theoretical framework…

Machine Learning · Computer Science 2025-10-13 Yuichi Kondo , Hideaki Iiduka