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In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
Hyperparameter optimization in machine learning is often achieved using naive techniques that only lead to an approximate set of hyperparameters. Although techniques such as Bayesian optimization perform an intelligent search on a given…
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…
Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy-preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential…
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…
Bi-level optimization, especially the gradient-based category, has been widely used in the deep learning community including hyperparameter optimization and meta-knowledge extraction. Bi-level optimization embeds one problem within another…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community.…
A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…
Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…
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…
This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This…
This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not…
In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…
A simple bilevel variational problem where the lower level is a variational inequality while the upper level is an optimization problem is studied. We consider an inexact version of the lower problem, which guarantees enough regularity to…
The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…
In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in…
(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…