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Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several…

Machine Learning · Computer Science 2019-06-10 Zhenxun Zhuang , Ashok Cutkosky , Francesco Orabona

Establishing a fast rate of convergence for optimization methods is crucial to their applicability in practice. With the increasing popularity of deep learning over the past decade, stochastic gradient descent and its adaptive variants…

Optimization and Control · Mathematics 2022-01-03 Adityanarayanan Radhakrishnan , Mikhail Belkin , Caroline Uhler

We study distributed optimization algorithms for minimizing the average of \emph{heterogeneous} functions distributed across several machines with a focus on communication efficiency. In such settings, naively using the classical stochastic…

Machine Learning · Computer Science 2020-11-18 Ilqar Ramazanli , Han Nguyen , Hai Pham , Sashank J. Reddi , Barnabas Poczos

We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we…

Optimization and Control · Mathematics 2025-09-30 Erfan Yazdandoost Hamedani , Afrooz Jalilzadeh , Necdet Serhat Aybat

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

Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence…

Machine Learning · Computer Science 2025-07-03 Di Zhang , Yihang Zhang

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…

Signal Processing · Electrical Eng. & Systems 2020-07-10 Zhan Gao , Alec Koppel , Alejandro Ribeiro

We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter…

Machine Learning · Computer Science 2025-09-19 Jean-François Aujol , Jérémie Bigot , Camille Castera

The practical performance of online stochastic gradient descent algorithms is highly dependent on the chosen step size, which must be tediously hand-tuned in many applications. The same is true for more advanced variants of stochastic…

Optimization and Control · Mathematics 2015-11-10 Pierre-Yves Massé , Yann Ollivier

We propose a stochastic variant of the classical Polyak step-size (Polyak, 1987) commonly used in the subgradient method. Although computing the Polyak step-size requires knowledge of the optimal function values, this information is readily…

Optimization and Control · Mathematics 2021-03-23 Nicolas Loizou , Sharan Vaswani , Issam Laradji , Simon Lacoste-Julien

The generalized Lasso is a remarkably versatile and extensively utilized model across a broad spectrum of domains, including statistics, machine learning, and image science. Among the optimization techniques employed to address the…

Optimization and Control · Mathematics 2024-07-29 Xueying Zeng , Bin Shi

This work introduces a two-step stepsize schedule for stochastic gradient methods minimizing smooth strongly convex functions. We consider the setting where only stochastic gradient approximations, which are unbiased, of bounded variance,…

Optimization and Control · Mathematics 2025-12-01 Luwei Bai , Yang Zeng , Baoyu Zhou

This work considers stepsize schedules for gradient descent on smooth convex objectives. We extend the existing literature and propose a unified technique for constructing stepsizes with analytic bounds for an arbitrary number of…

Optimization and Control · Mathematics 2026-02-17 Zehao Zhang , Rujun Jiang

We consider strongly-convex-strongly-concave saddle point problems assuming we have access to unbiased stochastic estimates of the gradients. We propose a stochastic accelerated primal-dual (SAPD) algorithm and show that SAPD sequence,…

Optimization and Control · Mathematics 2024-09-04 Xuan Zhang , Necdet Serhat Aybat , Mert Gürbüzbalaban

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

Machine Learning · Computer Science 2018-02-02 Tianyi Lin , Linbo Qiao , Teng Zhang , Jiashi Feng , Bofeng Zhang

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

We provide a simple and generic adaptive restart scheme for convex optimization that is able to achieve worst-case bounds matching (up to constant multiplicative factors) optimal restart schemes that require knowledge of problem specific…

Optimization and Control · Mathematics 2020-08-18 Oliver Hinder , Miles Lubin

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of…

Numerical Analysis · Computer Science 2018-08-23 Michael P. Friedlander , Mark Schmidt

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…

Optimization and Control · Mathematics 2021-02-02 Zhi Li , Wei Shi , Ming Yan

We reconsider the stochastic (sub)gradient approach to the unconstrained primal L1-SVM optimization. We observe that if the learning rate is inversely proportional to the number of steps, i.e., the number of times any training pattern is…

Machine Learning · Computer Science 2014-01-28 Constantinos Panagiotakopoulos , Petroula Tsampouka