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This paper introduces \textit{online bilevel optimization} in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for online single-level algorithms to the bilevel setting.…

Optimization and Control · Mathematics 2024-07-10 Davoud Ataee Tarzanagh , Parvin Nazari , Bojian Hou , Li Shen , Laura Balzano

In traditional machine learning techniques, the degree of closeness between true and predicted values generally measures the quality of predictions. However, these learning algorithms do not consider prescription problems where the…

Machine Learning · Computer Science 2021-01-05 Mehmet Kolcu , Alper E. Murat

Strongly motivated from use in various fields including machine learning, the methodology of sparse optimization has been developed intensively so far. Especially, the recent advance of algorithms for solving problems with nonsmooth…

Optimization and Control · Mathematics 2023-04-21 Jan Harold Alcantara , Chieu Thanh Nguyen , Takayuki Okuno , Akiko Takeda , Jein-Shan Chen

The most common procedure to solve a linear bilevel problem in the PES community is, by far, to transform it into an equivalent single-level problem by replacing the lower level with its KKT optimality conditions. Then, the complementarity…

Optimization and Control · Mathematics 2018-09-28 Salvador Pineda , Juan Miguel Morales

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

Machine Learning · Statistics 2024-12-10 Ieva Petrulionyte , Julien Mairal , Michael Arbel

Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…

Optimization and Control · Mathematics 2020-08-28 Filip Hanzely

We present a novel unified bilevel optimization-based framework, \textsf{PARL}, formulated to address the recently highlighted critical issue of policy alignment in reinforcement learning using utility or preference-based feedback. We…

Machine Learning · Computer Science 2024-05-02 Souradip Chakraborty , Amrit Singh Bedi , Alec Koppel , Dinesh Manocha , Huazheng Wang , Mengdi Wang , Furong Huang

This paper proposes an asymmetric perturbation technique for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Perturbing payoffs or values is known to be…

Optimization and Control · Mathematics 2026-02-16 Kenshi Abe , Mitsuki Sakamoto , Kaito Ariu , Atsushi Iwasaki

We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…

Computer Vision and Pattern Recognition · Computer Science 2011-12-06 Jan Lellmann , Frank Lenzen , Christoph Schnörr

One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…

Statistics Theory · Mathematics 2021-01-08 Neil K. Chada , Claudia Schillings , Xin T. Tong , Simon Weissmann

In this work we propose an improvement of the $x$-space algorithm developed for solving a class of min--max bilevel optimization problems (Tang Y., Richard J.P.P., Smith J.C. (2016), A class of algorithms for mixed-integer bilevel min--max…

Optimization and Control · Mathematics 2021-05-19 Kübra Tanınmış , Necati Aras , İ. Kuban Altınel

We analyse a general class of bilevel problems, in which the upper-level problem consists in the minimization of a smooth objective function and the lower-level problem is to find the fixed point of a smooth contraction map. This type of…

Machine Learning · Statistics 2023-11-17 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo

Unsupervised binary representation allows fast data retrieval without any annotations, enabling practical application like fast person re-identification and multimedia retrieval. It is argued that conflicts in binary space are one of the…

Computer Vision and Pattern Recognition · Computer Science 2020-11-23 Fangrui Liu , Zheng Liu

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

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…

Optimization and Control · Mathematics 2016-05-18 Xuan Liu , Zuyi Li

In this paper, we formulate the hyperparameter tuning problem in machine learning as a bilevel program. The bilevel program is solved using a micro genetic algorithm that is enhanced with a linear program. While the genetic algorithm…

Machine Learning · Computer Science 2024-07-02 Ankur Sinha , Paritosh Pankaj

This paper considers a class of distributed bilevel optimization (DBO) problems with a coupled inner-level subproblem. Existing approaches typically rely on hypergradient estimations involving computationally expensive Hessian evaluation.…

Optimization and Control · Mathematics 2026-02-27 Youcheng Niu , Jinming Xu , Ying Sun , Li Chai , Jiming Chen

This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes…

Machine Learning · Statistics 2026-03-03 Giovanni S. Alberti , Ernesto De Vito , Tapio Helin , Matti Lassas , Luca Ratti , Matteo Santacesaria

Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice…

Machine Learning · Statistics 2025-10-08 Nicholas H. Nelsen , Houman Owhadi , Andrew M. Stuart , Xianjin Yang , Zongren Zou