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Designs which are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values. This mean…

Statistics Theory · Mathematics 2026-03-05 Douglas P. Wiens

For decision making under uncertainty, min-max regret has been established as a popular methodology to find robust solutions. In this approach, we compare the performance of our solution against the best possible performance had we known…

Optimization and Control · Mathematics 2021-11-25 Marc Goerigk , Michael Hartisch

We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…

Machine Learning · Computer Science 2024-10-10 Dimitris Bertsimas , Yu Ma

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

Information Theory · Computer Science 2017-01-11 Mohamed Suliman , Tarig Ballal , Tareq Y. Al-Naffouri

An important problem in sequential decision-making under uncertainty is to use limited data to compute a safe policy, i.e., a policy that is guaranteed to perform at least as well as a given baseline strategy. In this paper, we develop and…

Machine Learning · Statistics 2016-07-14 Marek Petrik , Yinlam Chow , Mohammad Ghavamzadeh

Multi-criteria decision-making often requires finding a small representative set from the database. A recently proposed method is the regret minimization set (RMS) query. RMS returns a size $r$ subset $S$ of dataset $D$ that minimizes the…

Machine Learning · Computer Science 2022-03-10 Xingxing Xiao , Jianzhong Li

Experimental designs that are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values.…

Statistics Theory · Mathematics 2026-04-27 Rui Hu , Douglas P. Wiens

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

Optimization and Control · Mathematics 2015-08-21 Bram L. Gorissen

This paper presents a novel feature of the kernel-based system identification method. We prove that the regularized kernel-based approach for the estimation of a finite impulse response is equivalent to a robust least-squares problem with a…

Optimization and Control · Mathematics 2021-05-27 Mohammad Khosravi , Roy S. Smith

We consider the problem of selecting a subset of points from a dataset of $n$ unlabeled examples for labeling, with the goal of training a multiclass classifier. To address this, we build upon the regret minimization framework introduced by…

Machine Learning · Computer Science 2026-02-27 Youguang Chen , George Biros

We consider the setting of iterative learning control, or model-based policy learning in the presence of uncertain, time-varying dynamics. In this setting, we propose a new performance metric, planning regret, which replaces the standard…

Machine Learning · Computer Science 2021-03-01 Naman Agarwal , Elad Hazan , Anirudha Majumdar , Karan Singh

Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…

Optimization and Control · Mathematics 2022-01-14 Marc Goerigk , Mohammad Khosravi

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

Machine Learning · Statistics 2020-02-10 Muhammad Osama , Dave Zachariah , Peter Stoica

This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer…

Data Structures and Algorithms · Computer Science 2016-12-21 Lucas Assunção , Thiago F. Noronha , Andréa Cynthia Santos , Rafael Andrade

We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the…

Machine Learning · Statistics 2013-02-13 Wei Han , Alexander Rakhlin , Karthik Sridharan

We propose a Binary Robust Least Squares (BRLS) model that encompasses key robust least squares formulations, such as those involving uncertain binary labels and adversarial noise constrained within a hypercube. We show that the geometric…

Optimization and Control · Mathematics 2025-10-14 Yang Zhou , Xiaojun Chen

We study the problem of regret minimization in partially observable linear quadratic control systems when the model dynamics are unknown a priori. We propose ExpCommit, an explore-then-commit algorithm that learns the model Markov…

Machine Learning · Computer Science 2020-03-10 Sahin Lale , Kamyar Azizzadenesheli , Babak Hassibi , Anima Anandkumar

Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions…

Machine Learning · Computer Science 2025-08-11 Víctor Bucarey , Sophia Calderón , Gonzalo Muñoz , Frederic Semet

We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…

Optimization and Control · Mathematics 2021-10-05 Xiangyi Fan , Grani A. Hanasusanto

We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose…

Optimization and Control · Mathematics 2026-04-21 Feras Al Taha , Eilyan Bitar