Related papers: Bilevel optimization with a multi-objective lower-…

Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…

In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper-…

Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…

We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into account coil manufacturing errors. By modeling coil errors independently from the coil…

We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…

Multiobjective stochastic programming is a field well located to tackle problems arising in emergencies, given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in this…

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision…

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…

A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…

Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…

Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step,…

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,…

Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained…

The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…

Adversarial machine learning concerns situations in which learners face attacks from active adversaries. Such scenarios arise in applications such as spam email filtering, malware detection and fake-image generation, where security methods…

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

In recent years, decentralized bilevel optimization problems have received increasing attention in the networking and machine learning communities thanks to their versatility in modeling decentralized learning problems over peer-to-peer…