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Multi-task learning through composite loss functions is fundamental to modern deep learning, yet optimizing competing objectives remains challenging. We present new theoretical and practical approaches for addressing directional conflicts…

Machine Learning · Computer Science 2025-09-22 Sifan Wang , Ananyae Kumar Bhartari , Bowen Li , Paris Perdikaris

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

Optimization and Control · Mathematics 2025-10-07 Rajiv Sambharya , Jinho Bok , Nikolai Matni , George Pappas

We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing…

Programming Languages · Computer Science 2026-01-08 Ziyi Yang , George Pîrlea , Ilya Sergey

The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…

Optimization and Control · Mathematics 2024-02-08 Nikita Doikov , Sebastian U. Stich , Martin Jaggi

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the…

We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…

Optimization and Control · Mathematics 2017-06-21 Jérôme Bolte , Shoham Sabach , Marc Teboulle , Yakov Vaisbourd

Learning to optimize - the idea that we can learn from data algorithms that optimize a numerical criterion - has recently been at the heart of a growing number of research efforts. One of the most challenging issues within this approach is…

Machine Learning · Computer Science 2018-02-21 Louis Faury , Flavian Vasile

We introduce a machine-learning framework to learn the hyperparameter sequence of first-order methods (e.g., the step sizes in gradient descent) to quickly solve parametric convex optimization problems. Our computational architecture…

Optimization and Control · Mathematics 2024-12-23 Rajiv Sambharya , Bartolomeo Stellato

Pretrained vision-language models (VLMs) such as CLIP have shown impressive generalization capability in downstream vision tasks with appropriate text prompts. Instead of designing prompts manually, Context Optimization (CoOp) has been…

Computer Vision and Pattern Recognition · Computer Science 2023-02-15 Chengcheng Ma , Yang Liu , Jiankang Deng , Lingxi Xie , Weiming Dong , Changsheng Xu

First-order optimization methods, such as SGD and Adam, are widely used for training large-scale deep neural networks due to their computational efficiency and robust performance. However, relying solely on gradient information, these…

Machine Learning · Computer Science 2025-07-29 Yue Hu , Zanxia Cao , Yingchao Liu

Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…

Optimization and Control · Mathematics 2023-07-18 Wei Liu , Qihang Lin , Yangyang Xu

Any gradient descent optimization requires to choose a learning rate. With deeper and deeper models, tuning that learning rate can easily become tedious and does not necessarily lead to an ideal convergence. We propose a variation of the…

Machine Learning · Statistics 2018-04-10 Mathieu Ravaut , Satya Gorti

Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…

Optimization and Control · Mathematics 2023-04-28 V. S. Amaral , R. Andreani , E. G. Birgin , D. S. Marcondes , J. M. Martínez

We introduce in this paper an optimal first-order method that allows an easy and cheap evaluation of the local Lipschitz constant of the objective's gradient. This constant must ideally be chosen at every iteration as small as possible,…

Optimization and Control · Mathematics 2012-07-18 Michel Baes , Michael Buergisser

Stochastic approximation (SA) algorithms have been widely applied in minimization problems when the loss functions and/or the gradient information are only accessible through noisy evaluations. Stochastic gradient (SG) descent---a…

Optimization and Control · Mathematics 2019-08-26 Jingyi Zhu , Long Wang , James C. Spall

This paper studies the empirical efficacy and benefits of using projection-free first-order methods in the form of Conditional Gradients, a.k.a. Frank-Wolfe methods, for training Neural Networks with constrained parameters. We draw…

Machine Learning · Computer Science 2020-10-22 Sebastian Pokutta , Christoph Spiegel , Max Zimmer

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…

Optimization and Control · Mathematics 2022-07-15 Luis Briceño-Arias , Nelly Pustelnik

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

Machine Learning · Computer Science 2021-11-09 Guan-Horng Liu , Tianrong Chen , Evangelos A. Theodorou

We study the training dynamics of gradient descent in a softmax self-attention layer trained to perform linear regression and show that a simple first-order optimization algorithm can converge to the globally optimal self-attention…

Machine Learning · Computer Science 2026-03-03 Gautam Goel , Mahdi Soltanolkotabi , Peter Bartlett

Adaptive gradient methods are computationally efficient and converge quickly, but they often suffer from poor generalization. In contrast, second-order methods enhance convergence and generalization but typically incur high computational…

Machine Learning · Computer Science 2025-06-11 Hyunseok Seung , Jaewoo Lee , Hyunsuk Ko