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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

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

Optimization and Control · Mathematics 2024-03-15 Nazanin Abolfazli , Ruichen Jiang , Aryan Mokhtari , Erfan Yazdandoost Hamedani

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

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…

Optimization and Control · Mathematics 2025-11-27 Filippo Marini , Margherita Porcelli , Elisa Riccietti

We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…

Optimization and Control · Mathematics 2018-09-27 Mostafa Amini , Farzad Yousefian

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

Machine Learning · Statistics 2025-05-20 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo

Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…

Optimization and Control · Mathematics 2023-01-25 Yasmine Beck , Ivana Ljubić , Martin Schmidt

The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…

Machine Learning · Statistics 2018-04-06 Yuansi Chen , Chi Jin , Bin Yu

This paper studies convergence properties of inexact iterative solution schemes for bilevel optimization problems. Bilevel optimization problems emerge in control-aware design optimization, where the system design parameters are optimized…

Optimization and Control · Mathematics 2024-03-26 Torbjørn Cunis Ilya Kolmanovsky

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

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…

Optimization and Control · Mathematics 2024-02-13 Jeongyeol Kwon , Dohyun Kwon , Stephen Wright , Robert Nowak

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 been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

Machine Learning · Computer Science 2023-08-22 Siyuan Xu , Minghui Zhu

Handling uncertainty is critical for ensuring reliable decision-making in intelligent systems. Modern neural networks are known to be poorly calibrated, resulting in predicted confidence scores that are difficult to use. This article…

Machine Learning · Computer Science 2026-05-18 Gabriele Sanguin , Arjun Pakrashi , Marco Viola , Francesco Rinaldi

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 optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…

Optimization and Control · Mathematics 2026-03-03 Yuman Wu , Xiaochuan Gong , Jie Hao , Mingrui Liu

Two-level stochastic optimization formulations have become instrumental in a number of machine learning contexts such as continual learning, neural architecture search, adversarial learning, and hyperparameter tuning. Practical stochastic…

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

A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…

Optimization and Control · Mathematics 2018-12-05 Gernot Holler , Karl Kunisch , Richard C. Barnard

In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…

Optimization and Control · Mathematics 2017-02-15 Shoham Sabach , Shimrit Shtern

This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…

Optimization and Control · Mathematics 2026-02-06 Mattia Solla , Johannes O. Royset