English
Related papers

Related papers: A Discretization Approach for Bilevel Optimization…

200 papers

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…

Optimization and Control · Mathematics 2025-12-04 James Kotary , Himanshu Sharma , Ethan King , Draguna Vrabie , Ferdinando Fioretto , Jan Drgona

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

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

Optimization and Control · Mathematics 2024-02-01 Digvijay Boob , Qi Deng , Guanghui Lan

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

This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…

Optimization and Control · Mathematics 2025-11-06 Dhaval Pujara , Ankur Sinha

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

In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual…

Optimization and Control · Mathematics 2022-11-22 Quanqi Hu , Yongjian Zhong , Tianbao Yang

Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…

Optimization and Control · Mathematics 2025-04-25 Nazanin Abolfazli , Sina Sharifi , Mahyar Fazlyab , Erfan Yazdandoost Hamedani

This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for…

Optimization and Control · Mathematics 2024-03-06 Jiulin Wang , Xu Shi , Rujun Jiang

Several important problem settings within the literature of reinforcement learning (RL), such as meta-learning, hierarchical learning, and RL from human feedback (RL-HF), can be modelled as bilevel RL problems. A lot has been achieved in…

Machine Learning · Computer Science 2026-02-03 Naman Saxena , Vaneet Aggarwal

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

We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with…

Machine Learning · Computer Science 2026-01-08 Ray Zirui Zhang , Christopher E. Miles , Xiaohui Xie , John S. Lowengrub

Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…

Machine Learning · Computer Science 2024-11-05 Xiaoyu Wang , Rui Pan , Renjie Pi , Jipeng Zhang

This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…

Optimization and Control · Mathematics 2021-06-16 Prashant Khanduri , Siliang Zeng , Mingyi Hong , Hoi-To Wai , Zhaoran Wang , Zhuoran Yang

Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…

Optimization and Control · Mathematics 2026-05-05 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo , Alain Zemkoho

Bilevel optimization is characterized by a two-level optimization structure, where the upper-level problem is constrained by optimal lower-level solutions, and such structures are prevalent in real-world problems. The constraint by optimal…

Machine Learning · Computer Science 2025-05-29 Ruth Wan Theng Chew , Quoc Phong Nguyen , Bryan Kian Hsiang Low

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

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…

Machine Learning · Computer Science 2023-03-16 Meng Ding , Mingxi Lei , Yunwen Lei , Di Wang , Jinhui Xu

This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant…

Machine Learning · Computer Science 2025-01-16 Xiaochuan Gong , Jie Hao , Mingrui Liu

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the…

Optimization and Control · Mathematics 2023-11-08 Tommaso Giovannelli , Griffin Dean Kent , Luis Nunes Vicente