Related papers: A bilevel learning approach for optimal observatio…

Bilevel optimization, the problem of minimizing a value function which involves the arg-minimum of another function, appears in many areas of machine learning. In a large scale empirical risk minimization setting where the number of samples…

Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…

Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks,…

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…

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…

This chapter presents a self-contained approach of variational analysis and generalized differentiation to deriving necessary optimality in problems of bilevel optimization with Lipschitzian data. We mainly concentrate on optimistic models,…

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…

We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem…

A bilevel optimization problem consists of two optimization problems nested as an upper- and a lower-level problem, in which the optimality of the lower-level problem defines a constraint for the upper-level problem. This paper considers…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Bilevel optimization is a popular two-level hierarchical optimization, which has been widely applied to many machine learning tasks such as hyperparameter learning, meta learning and continual learning. Although many bilevel optimization…

In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…

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…

Bilevel optimization is a popular hierarchical model in machine learning, and has been widely applied to many machine learning tasks such as meta learning, hyperparameter learning and policy optimization. Although many bilevel optimization…

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…

Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…

In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper-…

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…

Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex…