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Bilevel programming is one of the very active areas of research with many real-life applications in economics and engineering. Bilevel problems are hierarchical problems consisting of lower-level and upper-level problems, respectively. The…
Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…
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…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the…
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…
Simple bilevel problems are optimization problems in which we want to find an optimal solution to an inner problem that minimizes an outer objective function. Such problems appear in many machine learning and signal processing applications…
Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…
Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based…
In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…
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…
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…
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…
The main purpose of this paper is to close the gap between the optimal values of an infinite convex program and that of its biconjugate relaxation. It is shown that Slater and continuity-type conditions guarantee such a zero-duality gap.…
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…
Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions,…
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…
We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome…