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This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…

Optimization and Control · Mathematics 2025-07-30 Charles Dapogny , Julien Prando , Boris Thibert

We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…

Machine Learning · Computer Science 2017-07-05 Robert Chen , Brendan Lucier , Yaron Singer , Vasilis Syrgkanis

We consider global non-convex optimisation problems under uncertainty. In this setting, it is not possible to implement a desired solution exactly. Instead, any other solution within some distance to the intended solution may be…

Optimization and Control · Mathematics 2020-03-24 Martin Hughes , Marc Goerigk , Trivikram Dokka

Our focus is on robust recovery algorithms in statistical linear inverse problem. We consider two recovery routines - the much studied linear estimate originating from Kuks and Olman [42] and polyhedral estimate introduced in [37]. It was…

Statistics Theory · Mathematics 2023-09-14 Yannis Bekri , Anatoli Juditsky , Arkadi Nemirovski

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…

Optimization and Control · Mathematics 2025-01-28 Arjun Ramachandra , Napat Rujeerapaiboon , Melvyn Sim

This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with…

Statistics Theory · Mathematics 2026-02-24 Gökhan Gül

The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…

Optimization and Control · Mathematics 2025-05-28 Ling Liang , Zusen Xu , Kim-Chuan Toh , Jia-Jie Zhu

Classical stochastic control assumes perfect knowledge of the uncertainty affecting the plant. In practice, however, such information is often incomplete. To address this limitation, we consider a distributionally robust control (DRC)…

Systems and Control · Electrical Eng. & Systems 2026-05-06 Riccardo Cescon , Andrea Martin , Giancarlo Ferrari-Trecate

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

Machine Learning · Computer Science 2024-12-03 Maryam Aliakbarpour , Piotr Indyk , Ronitt Rubinfeld , Sandeep Silwal

In state estimation tasks, the usual assumption of exactly known disturbance distribution is often unrealistic and renders the estimator fragile in practice. The recently emerging Wasserstein distributionally robust state estimation (DRSE)…

Optimization and Control · Mathematics 2026-02-10 Yulin Feng , Xianyu Li , Steven X. Ding , Hao Ye , Chao Shang

We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…

Machine Learning · Statistics 2015-06-25 Roy Frostig , Rong Ge , Sham M. Kakade , Aaron Sidford

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…

Statistics Theory · Mathematics 2026-04-21 Alejandro Cholaquidis , Emilien Joly , Leonardo Moreno

We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…

Optimization and Control · Mathematics 2025-03-27 Jie Wang , Rui Gao , Yao Xie

The reliable deployment of neural networks in control systems requires rigorous robustness guarantees. In this paper, we obtain tight robustness certificates over convex attack sets for min-max representations of ReLU neural networks by…

Optimization and Control · Mathematics 2023-10-10 Brendon G. Anderson , Samuel Pfrommer , Somayeh Sojoudi

We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive…

Machine Learning · Computer Science 2017-07-04 Jonas Moritz Kohler , Aurelien Lucchi

This paper investigates probabilistic robustness of nonconvex-nonconcave minimax problems via the scenario approach. Specifically, under convex strategy sets for all players, inspired by recent advances in scenario optimization, we first…

Computer Science and Game Theory · Computer Science 2026-05-14 Huan Peng , Guanpu Chen , Karl Henrik Johansson

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

Numerical Analysis · Mathematics 2018-11-27 Truong-Vinh Hoang , Hermann G. Matthies

Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency…

Machine Learning · Computer Science 2024-05-29 Ha Manh Bui , Anqi Liu

Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In…

Machine Learning · Computer Science 2013-12-18 Khoat Than , Tu Bao Ho

A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $\alpha-$divergence distances, is proposed. Sion's minimax theorem is…

Other Statistics · Statistics 2016-08-24 Gökhan Gül , Abdelhak M. Zoubir