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Related papers: Distributionally Robust Regret Minimization

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We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer…

Computer Science and Game Theory · Computer Science 2013-02-26 Joseph Y. Halpern , Samantha Leung

We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a…

Optimization and Control · Mathematics 2019-12-24 Bart P. G. Van Parys , Peyman Mohajerin Esfahani , Daniel Kuhn

We study the problem of a decision maker who must provide the best possible treatment recommendation based on an experiment. The desirability of the outcome distribution resulting from the policy recommendation is measured through a…

Econometrics · Economics 2022-04-06 Anders Bredahl Kock , David Preinerstorfer , Bezirgen Veliyev

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well-known to suffer…

Computer Science and Game Theory · Computer Science 2016-11-04 Joseph Y. Halpern , Samantha Leung

The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without assuming convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many interesting…

Optimization and Control · Mathematics 2026-03-09 Immanuel M. Bomze , Daniel de Vicente , Abdel Lisser , Heng Zhang

We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…

Optimization and Control · Mathematics 2024-07-24 Rui Gao , Rohit Arora , Yizhe Huang

We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash…

Optimization and Control · Mathematics 2018-10-02 Soroosh Shafieezadeh-Abadeh , Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani

This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…

Optimization and Control · Mathematics 2023-01-13 Charles Dapogny , Franck Iutzeler , Andrea Meda , Boris Thibert

We study, to our knowledge, the first tractable multistage ex-ante distributionally robust regret optimization (DRRO) formulation for stochastic control. We consider finite-horizon LQR under common stage-law ambiguity: disturbances are…

Optimization and Control · Mathematics 2026-04-08 Lukas-Benedikt Fiechtner , Jose Blanchet

In this paper, we consider contextual stochastic optimization problems under endogenous uncertainty, where decisions affect the underlying distributions. To implement such decisions in practice, it is crucial to ensure that their outcomes…

Optimization and Control · Mathematics 2025-10-16 Jasone Ramírez-Ayerbe , Emma Frejinger

In clinical trials and other applications, we often see regions of the feature space that appear to exhibit interesting behaviour, but it is unclear whether these observed phenomena are reflected at the population level. Focusing on a…

Statistics Theory · Mathematics 2023-09-21 Henry W. J. Reeve , Timothy I. Cannings , Richard J. Samworth

In the Newsvendor problem, the goal is to guess the number that will be drawn from some distribution, with asymmetric consequences for guessing too high vs. too low. In the data-driven version, the distribution is unknown, and one must work…

Machine Learning · Statistics 2026-01-05 Zhuoxin Chen , Will Ma

This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be…

Optimization and Control · Mathematics 2024-03-07 Sergey S. Ketkov

We study the robust quickest change detection under unknown pre- and post-change distributions. To deal with uncertainties in the data-generating distributions, we formulate two data-driven ambiguity sets based on the Wasserstein distance,…

Statistics Theory · Mathematics 2022-04-28 Liyan Xie

We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation…

Optimization and Control · Mathematics 2025-12-11 Jisun Park , Vinit Ranjan , Bartolomeo Stellato

This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and…

Optimization and Control · Mathematics 2022-12-29 Xinlei Yi , Xiuxian Li , Tao Yang , Lihua Xie , Tianyou Chai , Karl H. Johansson

This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a…

Optimization and Control · Mathematics 2025-12-29 Zhengmiao Wang , Zhi-Wei Liu , Ming Chi , Xiaoling Wang , Housheng Su , Lintao Ye

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative…

Systems and Control · Electrical Eng. & Systems 2024-04-05 Siyi Wang , Zifan Wang , Xinlei Yi , Michael M. Zavlanos , Karl H. Johansson , Sandra Hirche

Distributionally Robust Optimization (DRO) is a worst-case approach to decision making when there is model uncertainty. It is also well known that for certain uncertainty sets, DRO is approximated by a regularized nominal problem. We show…

Optimization and Control · Mathematics 2026-05-08 Jun-ya Gotoh , Michael Jong Kim , Andrew E. B. Lim

We investigate the problem of cumulative regret minimization for individual sequence prediction with respect to the best expert in a finite family of size K under limited access to information. We assume that in each round, the learner can…

Statistics Theory · Mathematics 2022-10-06 El Mehdi Saad , G. Blanchard