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Dynamic games can be an effective approach to modeling interactive behavior between multiple non-cooperative agents and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose…

Systems and Control · Electrical Eng. & Systems 2022-09-19 Edward L. Zhu , Francesco Borrelli

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

Machine Learning · Computer Science 2015-03-19 Alexander Rakhlin , Ohad Shamir , Karthik Sridharan

Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

Machine Learning · Computer Science 2024-02-13 Anuraganand Sharma

We propose mS2GD: a method incorporating a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent (S2GD). We consider the problem of minimizing a strongly convex function…

Machine Learning · Computer Science 2016-04-20 Jakub Konečný , Jie Liu , Peter Richtárik , Martin Takáč

Neural networks are usually trained by some form of stochastic gradient descent (SGD)). A number of strategies are in common use intended to improve SGD optimization, such as learning rate schedules, momentum, and batching. These are…

Neural and Evolutionary Computing · Computer Science 2015-08-13 Thomas M. Breuel

Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…

Machine Learning · Computer Science 2016-02-29 Thomas Hofmann , Aurelien Lucchi , Simon Lacoste-Julien , Brian McWilliams

The goal in this paper is to approximate the Price of Stability (PoS) in stochastic Nash games using stochastic approximation (SA) schemes. PoS is amongst the most popular metrics in game theory and provides an avenue for estimating the…

Optimization and Control · Mathematics 2023-10-31 Afrooz Jalilzadeh , Farzad Yousefian , Mohammadjavad Ebrahimi

This work presents stochastic optimization methods targeted at least-squares problems involving Monte Carlo integration. While the most common approach to solving these problems is to apply stochastic gradient descent (SGD) or similar…

Optimization and Control · Mathematics 2018-04-27 Gustavo T. Pfeiffer , Yoichi Sato

Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…

Optimization and Control · Mathematics 2019-01-28 Fabian Pedregosa , Kilian Fatras , Mattia Casotto

This paper considers a stochastic Nash game in which each player minimizes an expectation valued composite objective. We make the following contributions. (I) Under suitable monotonicity assumptions on the concatenated gradient map, we…

Optimization and Control · Mathematics 2020-05-25 Jinlong Lei , Uday V. Shanbhag

We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…

Machine Learning · Computer Science 2019-09-17 Luo Luo , Cheng Chen , Yujun Li , Guangzeng Xie , Zhihua Zhang

Despite the recent growth of theoretical studies and empirical successes of neural networks, gradient backpropagation is still the most widely used algorithm for training such networks. On the one hand, we have deterministic or full…

Machine Learning · Computer Science 2023-10-20 Pascal Junior Tikeng Notsawo

The $\ell_p$ regularization problem with $0< p< 1$ has been widely studied for finding sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. The proximal gradient…

Optimization and Control · Mathematics 2017-08-24 Yaohua Hu , Chong Li , Kaiwen Meng , Xiaoqi Yang

Stochastic gradient descent-ascent (SGDA) is one of the main workhorses for solving finite-sum minimax optimization problems. Most practical implementations of SGDA randomly reshuffle components and sequentially use them (i.e.,…

Optimization and Control · Mathematics 2023-02-21 Hanseul Cho , Chulhee Yun

Deep learning is built on the foundational guarantee that gradient descent on an objective function converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, that exhibit multiple…

Machine Learning · Computer Science 2019-05-14 Alistair Letcher , David Balduzzi , Sebastien Racaniere , James Martens , Jakob Foerster , Karl Tuyls , Thore Graepel

The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…

Numerical Analysis · Mathematics 2020-10-05 Arnulf Jentzen , Philippe von Wurstemberger

This paper considers convex optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for…

Optimization and Control · Mathematics 2015-06-16 Aryan Mokhtari , Alejandro Ribeiro

This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…

Computational Physics · Physics 2015-09-07 Robert L. Gates , Maximilian R. Bittens

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Optimization and Control · Mathematics 2023-08-15 Da Li , Jingjing Wu , Qingrun Zhang

In this paper, we propose a variable grouping method based on cooperative coevolution for large-scale multi-objective problems (LSMOPs), named Linkage Measurement Minimization (LMM). And for the sub-problem optimization stage, a hybrid…

Neural and Evolutionary Computing · Computer Science 2022-08-30 Rui Zhong , Masaharu Munetomo