Related papers: Bilevel Optimization and Variational Analysis
Hyperparameter tuning is an active area of research in machine learning, where the aim is to identify the optimal hyperparameters that provide the best performance on the validation set. Hyperparameter tuning is often achieved using naive…
In this article, we investigate a time-optimal state-constrained bilevel optimal control problem whose lower-level dynamics feature a sweeping control process involving a {\it truncated normal cone}. By bilevel, it is meant that the…
Real world problems always have different multiple solutions. For instance, optical engineers need to tune the recording parameters to get as many optimal solutions as possible for multiple trials in the varied-line-spacing holographic…
Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of Karush--Kuhn--Tucker-type necessary optimality conditions in order to characterize local minimizers.…
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…
We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…
We analyze a bilinear optimal control problem for the Stokes--Brinkman equations: the control variable enters the state equations as a coefficient. In two- and three-dimensional Lipschitz domains, we perform a complete continuous analysis…
In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of…
While stochastic bilevel optimization methods have been extensively studied for addressing large-scale nested optimization problems in machine learning, it remains an open question whether the optimal complexity bounds for solving bilevel…
We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in…
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…
Bilevel optimization have gained growing interests, with numerous applications found in meta learning, minimax games, reinforcement learning, and nested composition optimization. This paper studies the problem of distributed bilevel…
We discuss the multilevel control problem for linear dynamical systems, consisting in designing a piece-wise constant control function taking values in a finite-dimensional set. In particular, we provide a complete characterization of…
This PhD thesis presents a distributional view of optimization in place of a worst-case perspective. We motivate this view with an investigation of the failure point of classical optimization. Subsequently we consider the optimization of a…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…