Related papers: A Brief Introduction to Robust Bilevel Optimizatio…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method to produce solutions that are immunized against uncertainty. The main focus in robust…
It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
Portfolio optimization has been a major topic of research in finance, as it has a significant impact on investment profit. In this paper, we investigate the problem of data uncertainty in convex multi-objective portfolio optimization. We…
In this work, we consider the bilevel optimization problem on Riemannian manifolds. We inspect the calculation of the hypergradient of such problems on general manifolds and thus enable the utilization of gradient-based algorithms to solve…
Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…
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…
Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…
Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…
In strategic scenarios where decision-makers operate at different hierarchical levels, traditional optimization methods are often inadequate for handling uncertainties from incomplete information or unpredictable external factors. To fill…
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 paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…
Lecture Notes based on the course given at Toulouse School of Economics, on Fall 2024. It contains a quick introduction to the field of bilevel optimization, following a perspective from Variational Analysis.
In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the…
Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty…
Due to the large number of submissions that more and more conferences experience, finding an automatized way to well distribute the submitted papers among reviewers has become necessary. We model the peer-reviewing matching problem as a…
We consider a network design and expansion problem, where we need to make a capacity investment now, such that uncertain future demand can be satisfied as closely as possible. To use a robust optimization approach, we need to construct an…