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Adaptive gradient methods are typically used for training over-parameterized models. To better understand their behaviour, we study a simplistic setting -- smooth, convex losses with models over-parameterized enough to interpolate the data.…

Machine Learning · Computer Science 2021-02-22 Sharan Vaswani , Issam Laradji , Frederik Kunstner , Si Yi Meng , Mark Schmidt , Simon Lacoste-Julien

Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…

Numerical Analysis · Mathematics 2021-05-14 Kristian Debrabant , Giovanni Samaey , Przemysław Zieliński

In this paper we propose stochastic gradient-free methods and accelerated methods with momentum for solving stochastic optimization problems. All these methods rely on stochastic directions rather than stochastic gradients. We analyze the…

Optimization and Control · Mathematics 2020-01-15 Xiaopeng Luo , Xin Xu

Momentum methods, including heavy-ball~(HB) and Nesterov's accelerated gradient~(NAG), are widely used in training neural networks for their fast convergence. However, there is a lack of theoretical guarantees for their convergence and…

Machine Learning · Computer Science 2022-04-19 Xin Liu , Wei Tao , Zhisong Pan

In this work, we propose new adaptive step size strategies that improve several stochastic gradient methods. Our first method (StoPS) is based on the classical Polyak step size (Polyak, 1987) and is an extension of the recent development of…

Machine Learning · Computer Science 2022-08-11 Samuel Horváth , Konstantin Mishchenko , Peter Richtárik

We take a Hamiltonian-based perspective to generalize Nesterov's accelerated gradient descent and Polyak's heavy ball method to a broad class of momentum methods in the setting of (possibly) constrained minimization in Euclidean and…

Optimization and Control · Mathematics 2020-11-17 Jelena Diakonikolas , Michael I. Jordan

This work characterizes the benefits of averaging schemes widely used in conjunction with stochastic gradient descent (SGD). In particular, this work provides a sharp analysis of: (1) mini-batching, a method of averaging many samples of a…

Machine Learning · Statistics 2018-08-01 Prateek Jain , Sham M. Kakade , Rahul Kidambi , Praneeth Netrapalli , Aaron Sidford

In this work we investigate stochastic non-convex optimization problems where the objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such…

Optimization and Control · Mathematics 2021-11-02 Kfir Y. Levy , Ali Kavis , Volkan Cevher

This monograph covers some recent advances in a range of acceleration techniques frequently used in convex optimization. We first use quadratic optimization problems to introduce two key families of methods, namely momentum and nested…

Optimization and Control · Mathematics 2024-09-26 Alexandre d'Aspremont , Damien Scieur , Adrien Taylor

Heavy Ball (HB) nowadays is one of the most popular momentum methods in non-convex optimization. It has been widely observed that incorporating the Heavy Ball dynamic in gradient-based methods accelerates the training process of modern…

Optimization and Control · Mathematics 2023-08-30 Jun-Kun Wang , Chi-Heng Lin , Andre Wibisono , Bin Hu

Policy gradient (PG) methods are popular and efficient for large-scale reinforcement learning due to their relative stability and incremental nature. In recent years, the empirical success of PG methods has led to the development of a…

Machine Learning · Computer Science 2022-05-24 Yuhao Ding , Junzi Zhang , Javad Lavaei

It has been experimentally observed that distributed implementations of mini-batch stochastic gradient descent (SGD) algorithms exhibit speedup saturation and decaying generalization ability beyond a particular batch-size. In this work, we…

Machine Learning · Computer Science 2018-01-09 Dong Yin , Ashwin Pananjady , Max Lam , Dimitris Papailiopoulos , Kannan Ramchandran , Peter Bartlett

The Heavy Ball Method, proposed by Polyak over five decades ago, is a first-order method for optimizing continuous functions. While its stochastic counterpart has proven extremely popular in training deep networks, there are almost no known…

Machine Learning · Computer Science 2021-02-16 Jun-Kun Wang , Jacob Abernethy

This paper focus on the convergence of stochastic approximation with Nesterov momentum. Nesterov acceleration has proven effective in machine learning for its ability to reduce computational complexity. The issue of delayed information in…

Optimization and Control · Mathematics 2024-06-11 Zhang Ming-Kun

This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…

Optimization and Control · Mathematics 2021-10-15 Shengjun Zhang , Colleen P. Bailey

We develop a new parallel algorithm for minimizing Lipschitz, convex functions with a stochastic subgradient oracle. The total number of queries made and the query depth, i.e., the number of parallel rounds of queries, match the prior…

Optimization and Control · Mathematics 2024-06-12 Arun Jambulapati , Aaron Sidford , Kevin Tian

We introduce a new, high-throughput, synchronous, distributed, data-parallel, stochastic-gradient-descent learning algorithm. This algorithm uses amortized inference in a compute-cluster-specific, deep, generative, dynamical model to…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-03-14 Michael Teng , Frank Wood

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

Machine Learning · Computer Science 2017-11-23 Haiping Huang , Taro Toyoizumi

Gradient optimization algorithms using epochs, that is those based on stochastic gradient descent without replacement (SGDo), are predominantly used to train machine learning models in practice. However, the mathematical theory of SGDo and…

Machine Learning · Computer Science 2025-12-05 Stefan Perko

This paper delves into the realm of stochastic optimization for compositional minimax optimization - a pivotal challenge across various machine learning domains, including deep AUC and reinforcement learning policy evaluation. Despite its…

Machine Learning · Computer Science 2023-12-13 Jin Liu , Xiaokang Pan , Junwen Duan , Hongdong Li , Youqi Li , Zhe Qu