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Although traditional optimization methods focus on finding a single optimal solution, most objective functions in modern machine learning problems, especially those in deep learning, often have multiple or infinite numbers of optima.…

Machine Learning · Computer Science 2022-02-18 Chengyue Gong , Lemeng Wu , Qiang Liu

Sequential computation via autoregressive generation can make difficult tasks learnable, but the generation order of intermediate states strongly affects whether training succeeds. We address the problem of discovering a learning-friendly…

Machine Learning · Computer Science 2026-05-11 Yuta Sato , Kazuhiko Kawamoto , Hiroshi Kera

Reducing reinforcement learning to supervised learning is a well-studied and effective approach that leverages the benefits of compact function approximation to deal with large-scale Markov decision processes. Independently, the boosting…

Machine Learning · Computer Science 2023-01-26 Nataly Brukhim , Elad Hazan , Karan Singh

Boosting as gradient descent algorithms is one popular method in machine learning. In this paper a novel Boosting-type algorithm is proposed based on restricted gradient descent with structural sparsity control whose underlying dynamics are…

Machine Learning · Statistics 2017-04-18 Chendi Huang , Xinwei Sun , Jiechao Xiong , Yuan Yao

The success of deep learning over the past decade mainly relies on gradient-based optimisation and backpropagation. This paper focuses on analysing the performance of first-order gradient-based optimisation algorithms, gradient descent and…

Optimization and Control · Mathematics 2022-12-08 Behnam Mafakheri , Iman Shames , Jonathan H. Manton

Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so…

Machine Learning · Computer Science 2024-11-01 Timm Hess , Tinne Tuytelaars , Gido M. van de Ven

Ensemble learning of LLMs has emerged as a promising alternative to enhance performance, but existing approaches typically treat models as black boxes, combining the inputs or final outputs while overlooking the rich internal…

Boosting methods are highly popular and effective supervised learning methods which combine weak learners into a single accurate model with good statistical performance. In this paper, we analyze two well-known boosting methods, AdaBoost…

Machine Learning · Statistics 2013-07-05 Robert M. Freund , Paul Grigas , Rahul Mazumder

In the learning to learn (L2L) framework, we cast the design of optimization algorithms as a machine learning problem and use deep neural networks to learn the update rules. In this paper, we extend the L2L framework to zeroth-order (ZO)…

Machine Learning · Computer Science 2020-02-10 Yangjun Ruan , Yuanhao Xiong , Sashank Reddi , Sanjiv Kumar , Cho-Jui Hsieh

One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and…

Machine Learning · Computer Science 2021-01-01 Seth Neel , Aaron Roth , Giuseppe Vietri , Zhiwei Steven Wu

Learned Optimizers (LOs), a type of Meta-learning, have gained traction due to their ability to be parameterized and trained for efficient optimization. Traditional gradient-based methods incorporate explicit regularization techniques such…

Machine Learning · Computer Science 2025-10-13 Suraj Kumar Sahoo , Narayanan C Krishnan

Label ranking is a prediction task which deals with learning a mapping between an instance and a ranking (i.e., order) of labels from a finite set, representing their relevance to the instance. Boosting is a well-known and reliable ensemble…

Machine Learning · Computer Science 2020-09-24 Lihi Dery , Erez Shmueli

There is a growing cross-disciplinary effort in the broad domain of optimization and learning with streams of data, applied to settings where traditional batch optimization techniques cannot produce solutions at time scales that match the…

Optimization and Control · Mathematics 2021-11-29 Emiliano Dall'Anese , Andrea Simonetto , Stephen Becker , Liam Madden

This article introduces the concept of optimization learning, a methodology to design optimization proxies that learn the input/output mapping of parametric optimization problems. These optimization proxies are trustworthy by design: they…

Optimization and Control · Mathematics 2025-01-08 Pascal Van Hentenryck

Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which…

Machine Learning · Computer Science 2026-03-17 Qinzi Zhang , Ashok Cutkosky

For Mixture-of-Experts (MoE) models, an unbalanced expert load will lead to routing collapse or increased computational overhead. Existing methods commonly employ an auxiliary loss to encourage load balance, but a large auxiliary loss will…

Machine Learning · Computer Science 2024-08-29 Lean Wang , Huazuo Gao , Chenggang Zhao , Xu Sun , Damai Dai

Boosted decision trees are a very powerful machine learning technique. After introducing specific concepts of machine learning in the high-energy physics context and describing ways to quantify the performance and training quality of…

Data Analysis, Statistics and Probability · Physics 2022-06-22 Yann Coadou

Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems. However, computing gradients via implicit differentiation requires solving a linear system with Hessian terms, which is…

Machine Learning · Computer Science 2025-12-03 Zihao Zhao , Kai-Chia Mo , Shing-Hei Ho , Brandon Amos , Kai Wang

Decentralized solutions to finite-sum minimization are of significant importance in many signal processing, control, and machine learning applications. In such settings, the data is distributed over a network of arbitrarily-connected nodes…

Machine Learning · Computer Science 2019-11-14 Ran Xin , Soummya Kar , Usman A. Khan

These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…

Optimization and Control · Mathematics 2024-10-28 Charles Dossal , Samuel Hurault , Nicolas Papadakis