Related papers: Solving bilevel problems with products of upper- a…

This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…

Duality of linear programming is a standard approach to the classical weighted maximum matching problem. From an economic perspective, the dual variables can be regarded as prices of products and payoffs of buyers in a two-sided matching…

We study the feature-based newsvendor problem, in which a decision-maker has access to historical data consisting of demand observations and exogenous features. In this setting, we investigate feature selection, aiming to derive sparse,…

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…

Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…

The (gradient-based) bilevel programming framework is widely used in hyperparameter optimization and has achieved excellent performance empirically. Previous theoretical work mainly focuses on its optimization properties, while leaving the…

Usually, bilevel optimization problems need to be transformed into single-level ones in order to derive optimality conditions and solution algorithms. Among the available approaches, the replacement of the lower-level problem by means of…

Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for…

Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…

In this paper, we studied the federated bilevel optimization problem, which has widespread applications in machine learning. In particular, we developed two momentum-based algorithms for optimizing this kind of problem and established the…

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…

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…

In this paper, we exploit linear programming duality in the online setting (i.e., where input arrives on the fly) from the unique perspective of designing lower bounds on the competitive ratio. In particular, we provide a general technique…

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…

In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces,…

In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories,…

In this study, we consider a class of linear matroid interdiction problems, where the feasible sets for the upper-level decision-maker (referred to as a leader) and the lower-level decision-maker (referred to as a follower) are induced by…

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 problems comprise an upper level optimization task that contains a lower level optimization task as a constraint. While there is a significant and growing literature devoted to solving bilevel problems with single…