Related papers: A Brief Introduction to Robust Bilevel Optimizatio…

The goal of coreset selection in supervised learning is to produce a weighted subset of data, so that training only on the subset achieves similar performance as training on the entire dataset. Existing methods achieved promising results in…

This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (i) alter the uncertainty set, (ii) affect the…

Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…

We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…

Stochastic bilevel optimization tackles challenges involving nested optimization structures. Its fast-growing scale nowadays necessitates efficient distributed algorithms. In conventional distributed bilevel methods, each worker must…

Many real-world decision-making problems involve multiple decision-making stages and various objectives. Besides, most of the decisions need to be made before having complete knowledge about all aspects of the problem leaves some sort of…

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…

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…

This paper introduces \textit{online bilevel optimization} in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for online single-level algorithms to the bilevel setting.…

Bilevel optimization has recently attracted growing interests due to its wide applications in modern machine learning problems. Although recent studies have characterized the convergence rate for several such popular algorithms, it is still…

In this article, we extend our previous work (Applicable Analysis, 2024, pp. 1-25) on the steepest descent method for uncertain multiobjective optimization problems. While that study established local convergence, it did not address global…

In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included…

Gradient-based optimization has been critical to the success of machine learning, updating a single set of parameters to minimize a single loss. A growing number of applications rely on a generalization of this, where we have a bilevel or…

In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly accurate…

The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a…

Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many…

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…

Robust optimization is a method for optimization under uncertainties in engineering systems and designs for applications ranging from aeronautics to nuclear. In a robust design process, parameter variability (or uncertainty) is incorporated…

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…

The authors' paper in Optimization 63 (2014), 505-533, see Ref. [5], was the first one to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal…