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Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…

Optimization and Control · Mathematics 2021-02-22 Marc Goerigk , Stefan Lendl , Lasse Wulf

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,…

Optimization and Control · Mathematics 2021-03-22 Yassine Laguel , Jérôme Malick , Wim Ackooij

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems,…

Machine Learning · Computer Science 2022-12-29 Paul Vicol , Jonathan Lorraine , Fabian Pedregosa , David Duvenaud , Roger Grosse

Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…

Optimization and Control · Mathematics 2025-04-02 Parthasarathi Mondal , Akshay Kumar Ojha

A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various…

Machine Learning · Computer Science 2019-04-04 Chao Ning , Fengqi You

In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only…

Optimization and Control · Mathematics 2019-01-23 Trivikram Dokka , Marc Goerigk , Rahul Roy

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…

Optimization and Control · Mathematics 2023-11-16 Matthias J. Ehrhardt , Lindon Roberts

Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for…

Optimization and Control · Mathematics 2024-04-24 Youran Dong , Shiqian Ma , Junfeng Yang , Chao Yin

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

Optimization and Control · Mathematics 2025-01-28 Huaqing Zhang , Lesi Chen , Jing Xu , Jingzhao Zhang

This paper studies convergence properties of inexact iterative solution schemes for bilevel optimization problems. Bilevel optimization problems emerge in control-aware design optimization, where the system design parameters are optimized…

Optimization and Control · Mathematics 2024-03-26 Torbjørn Cunis Ilya Kolmanovsky

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)…

Optimization and Control · Mathematics 2025-04-14 Sepideh Samadi , Daniel Burbano , Farzad Yousefian

We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…

Machine Learning · Statistics 2018-10-30 Dimitris Bertsimas , Christopher McCord

In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…

Optimization and Control · Mathematics 2016-10-18 André Chassein , Marc Goerigk

In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual…

Optimization and Control · Mathematics 2022-11-22 Quanqi Hu , Yongjian Zhong , Tianbao Yang

The (gradient-based) bilevel programming framework is widely used in hyperparameter optimization and has achieved excellent performance empirically. Previous theoretical work mainly focuses on its optimization properties, while leaving the…

Machine Learning · Computer Science 2021-10-26 Fan Bao , Guoqiang Wu , Chongxuan Li , Jun Zhu , Bo Zhang

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…

Numerical Analysis · Mathematics 2020-07-06 Kjetil O. Lye , Siddhartha Mishra , Roberto Molinaro

Generative models form the backbone of modern machine learning, underpinning state-of-the-art systems in text, vision, and multimodal applications. While Maximum Likelihood Estimation has traditionally served as the dominant training…

Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…

Optimization and Control · Mathematics 2025-02-28 Yan Yang , Bin Gao , Ya-xiang Yuan

A standard type of uncertainty set in robust optimization is budgeted uncertainty, where an interval of possible values for each parameter is given and the total deviation from their lower bounds is bounded. In the two-stage setting,…

Optimization and Control · Mathematics 2026-02-19 Marc Goerigk , Dorothee Henke , Lasse Wulf

In robust optimization one seeks to make a decision under uncertainty, where the goal is to find the solution with the best worst-case performance. The set of possible realizations of the uncertain data is described by a so-called…

Optimization and Control · Mathematics 2022-01-25 Immanuel Bomze , Markus Gabl