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Bilevel optimization aims to optimize an outer objective function that depends on the solution to an inner optimization problem. It is routinely used in Machine Learning, notably for hyperparameter tuning. The conventional method to compute…

Machine Learning · Computer Science 2024-02-27 Zhenzhang Ye , Gabriel Peyré , Daniel Cremers , Pierre Ablin

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

Machine Learning · Computer Science 2018-03-08 Francesco Locatello , Rajiv Khanna , Joydeep Ghosh , Gunnar Rätsch

This paper aims to enhance the use of the Frank-Wolfe (FW) algorithm for training deep neural networks. Similar to any gradient-based optimization algorithm, FW suffers from high computational and memory costs when computing gradients for…

Machine Learning · Computer Science 2024-12-30 M. Rostami , S. S. Kia

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…

Machine Learning · Statistics 2019-02-01 Futoshi Futami , Zhenghang Cui , Issei Sato , Masashi Sugiyama

We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…

Optimization and Control · Mathematics 2022-07-12 Michael Arbel , Julien Mairal

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space…

Machine Learning · Statistics 2017-10-17 Edward Cheung , Yuying Li

This paper considers distributed stochastic optimization, in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network. Stochastic…

Optimization and Control · Mathematics 2022-08-09 Jie Hou , Xianlin Zeng , Gang Wang , Jian Sun , Jie Chen

Frank-Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of Machine Learning. The ability to work with cheap projection-free iterations and…

Machine Learning · Statistics 2015-10-27 Emanuele Frandi , Ricardo Nanculef , Stefano Lodi , Claudio Sartori , Johan A. K. Suykens

Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to…

Machine Learning · Statistics 2018-05-22 Yan Li , Chao Qu , Huan Xu

We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard…

Machine Learning · Computer Science 2019-02-01 Jarrid Rector-Brooks , Jun-Kun Wang , Barzan Mozafari

Bilevel optimization is widely applied in many machine learning tasks such as hyper-parameter learning, meta learning and reinforcement learning. Although many algorithms recently have been developed to solve the bilevel optimization…

Optimization and Control · Mathematics 2024-07-26 Feihu Huang

This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…

Optimization and Control · Mathematics 2025-07-11 Rujun Jiang , Xu Shi , Weizheng Song , Jiulin Wang

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…

Optimization and Control · Mathematics 2018-09-18 Yekini Shehu , Phan Tu Vuong , Alain Zemkoho

This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the…

Optimization and Control · Mathematics 2014-06-30 Guanghui Lan

In this paper, we consider non-convex optimization problems under \textit{unknown} yet safety-critical constraints. Such problems naturally arise in a variety of domains including robotics, manufacturing, and medical procedures, where it is…

Machine Learning · Computer Science 2020-06-25 Mohammad Fereydounian , Zebang Shen , Aryan Mokhtari , Amin Karbasi , Hamed Hassani

Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…

Optimization and Control · Mathematics 2024-11-12 Junyi Li , Heng Huang

Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…

Machine Learning · Computer Science 2025-02-04 Sheng Fang , Yong-Jin Liu , Wei Yao , Chengming Yu , Jin Zhang

Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…

Optimization and Control · Mathematics 2018-09-27 Harshal Kaushik , Farzad Yousefian

The Frank-Wolfe algorithm, a very first optimization method and also known as the conditional gradient method, was introduced by Frank and Wolfe in 1956. Due to its simple linear subproblems, the Frank-Wolfe algorithm has recently been…

Optimization and Control · Mathematics 2017-10-23 Hong-Kun Xu

Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…

Optimization and Control · Mathematics 2020-12-10 Matthias J. Ehrhardt , Lindon Roberts