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In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…
Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, meta-learning, and reinforcement learning. Recent results have shown that simple…
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…
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…
We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…
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…
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…
This paper studies the unconstrained nonconvex-strongly-convex bilevel optimization problem. A common approach to solving this problem is to alternately update the upper-level and lower-level variables using (biased) stochastic gradients or…
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 design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
This work focuses on addressing two major challenges in the context of large-scale nonconvex Bi-Level Optimization (BLO) problems, which are increasingly applied in machine learning due to their ability to model nested structures. These…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…
Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…
This article studies Gauss-Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
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…
For bilevel programs with a convex lower level program, the classical approach replaces the lower level program with its Karush-Kuhn-Tucker condition and solve the resulting mathematical program with complementarity constraint (MPCC). It is…
Bilevel programming has emerged as a valuable tool for hyperparameter selection, a central concern in machine learning. In a recent study by Ye et al. (2023), a value function-based difference of convex algorithm was introduced to address…