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Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in…

Machine Learning · Computer Science 2024-03-20 Heshan Fernando , Han Shen , Miao Liu , Subhajit Chaudhury , Keerthiram Murugesan , Tianyi Chen

Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the…

Neural and Evolutionary Computing · Computer Science 2013-10-08 Ankur Sinha , Pekka Malo , Kalyanmoy Deb

We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…

Optimization and Control · Mathematics 2025-04-14 Sepideh Samadi , Daniel Burbano , Farzad Yousefian

Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization…

Machine Learning · Computer Science 2021-08-03 Kaiyi Ji

When faced with multiple minima of an "inner-level" convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary "outer-level" convex objective of interest. Bilevel…

Optimization and Control · Mathematics 2024-10-10 Khanh-Hung Giang-Tran , Nam Ho-Nguyen , Dabeen Lee

Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the…

Machine Learning · Computer Science 2023-03-28 Hongchang Gao , Bin Gu , My T. Thai

We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…

Optimization and Control · Mathematics 2024-08-22 Yifan Hu , Jie Wang , Xin Chen , Niao He

Multi-Objective Bi-Level Optimization (MOBLO) addresses nested multi-objective optimization problems common in a range of applications. However, its multi-objective and hierarchical bilevel nature makes it notably complex. Gradient-based…

Optimization and Control · Mathematics 2024-06-11 Xinmin Yang , Wei Yao , Haian Yin , Shangzhi Zeng , Jin Zhang

Although application examples of multilevel optimization have already been discussed since the 1990s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine…

Optimization and Control · Mathematics 2021-10-27 Ryo Sato , Mirai Tanaka , Akiko Takeda

Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…

Optimization and Control · Mathematics 2024-11-28 Mathias Staudigl , Simon Weissmann , Tristan van Leeuwen

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 has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…

Optimization and Control · Mathematics 2024-12-25 Quan Xiao , Tianyi Chen

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…

Optimization and Control · Mathematics 2024-11-05 Andi Han , Bamdev Mishra , Pratik Jawanpuria , Akiko Takeda

Bilevel optimization (BO) is useful for solving a variety of important machine learning problems including but not limited to hyperparameter optimization, meta-learning, continual learning, and reinforcement learning. Conventional BO…

Machine Learning · Computer Science 2022-09-20 Mao Ye , Bo Liu , Stephen Wright , Peter Stone , Qiang Liu

Integrated learning and optimization (ILO) is a framework in contextual optimization which aims to train a predictive model for the probability distribution of the underlying problem data uncertainty, with the goal of enhancing the quality…

Optimization and Control · Mathematics 2026-01-26 Yuan Tao , Huifu Xu

It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to solving bilevel problems with continuous but nonconvex lower…

Optimization and Control · Mathematics 2023-05-04 Yasmine Beck , Daniel Bienstock , Martin Schmidt , Johannes Thürauf

Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…

Optimization and Control · Mathematics 2025-10-13 Hantao Nie , Jiaxiang Li , Zaiwen Wen

With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications…

Optimization and Control · Mathematics 2025-05-13 Tommaso Giovannelli , Griffin Dean Kent , Luis Nunes Vicente

In this paper, we study a class of bilevel optimization problems where the lower-level problem is a convex composite optimization model, which arises in various applications, including bilevel hyperparameter selection for regularized…

Optimization and Control · Mathematics 2026-05-13 Xiaoning Bai , Shangzhi Zeng , Jin Zhang , Lezhi Zhang

Existing decentralized stochastic optimization methods assume the lower-level loss function is strongly convex and the stochastic gradient noise has finite variance. These strong assumptions typically are not satisfied in real-world machine…

Machine Learning · Computer Science 2026-05-26 Xinwen Zhang , Yihan Zhang , Heng Liang , Hongchang Gao