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Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the…

Machine Learning · Statistics 2015-04-03 Dougal Maclaurin , David Duvenaud , Ryan P. Adams

We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…

Optimization and Control · Mathematics 2025-07-29 Yassine Kamri , Julien M. Hendrickx , François Glineur

This article proposes new perspectives for developing derivative based numerical algorithms, supported by the introduction of a generalized derivative operators. It demonstrates that these operators have the potential to enhance and extend…

General Mathematics · Mathematics 2026-01-13 Flavio Barbosa , Fernando Nogueira

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…

Optimization and Control · Mathematics 2013-01-08 Enlu Zhou , Jiaqiao Hu

In this paper, we deal with multiobjective composite optimization problems, where each objective function is a combination of smooth and possibly non-smooth functions. We first propose a parameter-dependent conditional gradient method to…

Optimization and Control · Mathematics 2024-10-25 Wang Chen , Liping Tang , Xinmin Yang

First order methods, which solely rely on gradient information, are commonly used in diverse machine learning (ML) and data analysis (DA) applications. This is attributed to the simplicity of their implementations, as well as low…

Machine Learning · Computer Science 2018-03-06 Sudhir B. Kylasa , Farbod Roosta-Khorasani , Michael W. Mahoney , Ananth Grama

Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…

Optimization and Control · Mathematics 2025-07-08 Vincent Roulet , Siddhartha Srinivasa , Maryam Fazel , Zaid Harchaoui

We present a new method for searching optimal hyperparameters among several tasks and several criteria. Multi-Task Multi Criteria method (MTMC) provides several Pareto-optimal solutions, among which one solution is selected with given…

Machine Learning · Computer Science 2020-02-18 Kirill Akhmetzyanov , Alexander Yuzhakov

A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…

Optimization and Control · Mathematics 2026-03-11 Serge Gratton , Philippe L. Toint

In this work, we develop first-order (Hessian-free) and zero-order (derivative-free) implementations of the Cubically regularized Newton method for solving general non-convex optimization problems. For that, we employ finite difference…

Optimization and Control · Mathematics 2023-09-06 Nikita Doikov , Geovani Nunes Grapiglia

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

Numerical Analysis · Mathematics 2015-11-13 Yunhui He , Yu Li , Hehu Xie

In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…

Optimization and Control · Mathematics 2022-08-03 Giacomo Borghi , Michael Herty , Lorenzo Pareschi

Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. Some evolutionary algorithms for multi-modal multi-objective optimization have been proposed in the literature. However,…

Neural and Evolutionary Computing · Computer Science 2020-10-02 Ryoji Tanabe , Hisao Ishibuchi

An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…

Numerical Analysis · Mathematics 2017-11-15 Cristian Barbarosie , Sérgio Lopes , Anca-Maria Toader

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

In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…

Optimization and Control · Mathematics 2015-10-27 Saeed Ghadimi , Guanghui Lan , Hongchao Zhang

The aim of global optimization is to find the global optimum of arbitrary classes of functions, possibly highly multimodal ones. In this paper we focus on the subproblem of global optimization for differentiable functions and we propose an…

Neural and Evolutionary Computing · Computer Science 2018-06-18 Louis Faury , Flavian Vasile , Clément Calauzènes , Olivier Fercoq

The performance of deep (reinforcement) learning systems crucially depends on the choice of hyperparameters. Their tuning is notoriously expensive, typically requiring an iterative training process to run for numerous steps to convergence.…

Machine Learning · Computer Science 2021-01-19 Vu Nguyen , Sebastian Schulze , Michael A Osborne

Machine learning (ML) methods offer a wide range of configurable hyperparameters that have a significant influence on their performance. While accuracy is a commonly used performance objective, in many settings, it is not sufficient.…

Machine Learning · Computer Science 2023-09-27 Romain Egele , Tyler Chang , Yixuan Sun , Venkatram Vishwanath , Prasanna Balaprakash

In this paper, we propose a unifying framework incorporating several momentum-related search directions for solving strongly monotone variational inequalities. The specific combinations of the search directions in the framework are made to…

Optimization and Control · Mathematics 2021-03-30 Kevin Huang , Shuzhong Zhang