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This study focuses on a Wasserstein-type gradient flow, which represents an optimization process of a continuous model of a Deep Neural Network (DNN). First, we establish the existence of a minimizer for an average loss of the model under…

Machine Learning · Computer Science 2024-04-16 Noboru Isobe

The use of network Newton methods for the decentralized optimization of a sum cost distributed through agents of a network is considered. Network Newton methods reinterpret distributed gradient descent as a penalty method, observe that the…

Optimization and Control · Mathematics 2015-04-24 Aryan Mokhtari , Qing Ling , Alejandro Ribeiro

In this paper, we study a variant of the quadratic penalty method for linearly constrained convex problems, which has already been widely used but actually lacks theoretical justification. Namely, the penalty parameter steadily increases…

Numerical Analysis · Mathematics 2017-11-30 Huan Li , Cong Fang , Zhouchen Lin

We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…

Optimization and Control · Mathematics 2026-03-16 Zepeng Wang , Juan Peypouquet

We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…

Machine Learning · Computer Science 2024-02-23 Zhiyu Zhang , Heng Yang , Ashok Cutkosky , Ioannis Ch. Paschalidis

Large language models (LLMs) exhibit remarkable capabilities across diverse tasks, yet aligning them efficiently and effectively with human expectations remains a critical challenge. This thesis advances LLM alignment by introducing novel…

Computation and Language · Computer Science 2025-06-12 Yuxin Jiang

Learned image compression (LIC) using deep learning architectures has seen significant advancements, yet standard rate-distortion (R-D) optimization often encounters imbalanced updates due to diverse gradients of the rate and distortion…

Image and Video Processing · Electrical Eng. & Systems 2025-03-19 Yichi Zhang , Zhihao Duan , Yuning Huang , Fengqing Zhu

While adaptive gradient methods are the workhorse of modern machine learning, sign-based optimization algorithms such as Lion and Muon have recently demonstrated superior empirical performance over AdamW in training large language models…

Machine Learning · Computer Science 2026-05-11 Dingzhi Yu , Hongyi Tao , Yuanyu Wan , Luo Luo , Lijun Zhang

Training - the optimisation of complex models - is traditionally performed through small, local, iterative updates [D. E. Rumelhart, G. E. Hinton, R. J. Williams, Nature 323, 533-536 (1986)]. Approximating solutions through truncated…

Machine Learning · Computer Science 2025-10-08 Reza T. Batley , Sourav Saha

A new learning algorithm proposed by Brandt and Lin for neural network [1], [2] has been shown to be mathematically equivalent to the conventional back-propagation learning algorithm, but has several advantages over the backpropagation…

Neural and Evolutionary Computing · Computer Science 2022-02-28 Feng Lin

In the convex optimization approach to online regret minimization, many methods have been developed to guarantee a $O(\sqrt{T})$ bound on regret for subdifferentiable convex loss functions with bounded subgradients, by using a reduction to…

Machine Learning · Computer Science 2016-09-20 Arthur Flajolet , Patrick Jaillet

This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It…

Optimization and Control · Mathematics 2020-11-18 Min Meng , Xiuxian Li

This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization…

Optimization and Control · Mathematics 2022-05-27 Anjali Parashar , Priyank Srivastava , Anuradha M. Annaswamy

This work presents a new algorithm for empirical risk minimization. The algorithm bridges the gap between first- and second-order methods by computing a search direction that uses a second-order-type update in one subspace, coupled with a…

Optimization and Control · Mathematics 2020-06-09 Majid Jahani , Mohammadreza Nazari , Rachael Tappenden , Albert S. Berahas , Martin Takáč

Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon…

Machine Learning · Computer Science 2022-05-17 Hancheng Min , Salma Tarmoun , Rene Vidal , Enrique Mallada

Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization (FL) -- a well-established…

Optimization and Control · Mathematics 2026-01-29 Runyu Zhang , Arvind Raghunathan , Jeff Shamma , Na Li

Optimization problems that include regularization functions in their objectives are regularly solved in many applications. When one seeks second-order methods for such problems, it may be desirable to exploit specific properties of some of…

Machine Learning · Computer Science 2023-07-11 Adeyemi D. Adeoye , Alberto Bemporad

Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do…

Machine Learning · Computer Science 2020-05-20 Daniel Golovin , John Karro , Greg Kochanski , Chansoo Lee , Xingyou Song , Qiuyi Zhang

Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…

Optimization and Control · Mathematics 2015-02-24 Jie Lu , Mikael Johansson

Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…

Machine Learning · Statistics 2020-02-21 Sattar Vakili , Sudeep Salgia , Qing Zhao
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