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Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

Machine Learning · Statistics 2024-11-05 Daniel Kuhn , Peyman Mohajerin Esfahani , Viet Anh Nguyen , Soroosh Shafieezadeh-Abadeh

We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL). The proposed distributional dynamic programming algorithms…

Machine Learning · Statistics 2024-07-22 Julian Gerstenberg , Ralph Neininger , Denis Spiegel

Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…

Optimization and Control · Mathematics 2026-02-09 Siyi Wang , Zifan Wang , Karl H. Johansson

In the Bayesian reinforcement learning (RL) setting, a prior distribution over the unknown problem parameters -- the rewards and transitions -- is assumed, and a policy that optimizes the (posterior) expected return is sought. A common…

Machine Learning · Computer Science 2021-09-27 Aviv Tamar , Daniel Soudry , Ev Zisselman

Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust…

Machine Learning · Computer Science 2025-05-05 Shixiong Wang , Haowei Wang , Xinke Li , Jean Honorio

The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions. In particular, we consider a sequence of $T\ge2$ data distributions $P_1,\ldots,P_T$ undergoing a…

Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…

Machine Learning · Computer Science 2020-06-08 Aurora Cobo Aguilera , Antonio Artés-Rodríguez , Fernando Pérez-Cruz , Pablo Martínez Olmos

Distributionally robust optimization (DRO)-based robust adaptive beamforming (RAB) enables enhanced robustness against model uncertainties, such as steering vector mismatches and interference-plus-noise covariance matrix estimation errors.…

Signal Processing · Electrical Eng. & Systems 2025-06-03 Kiarash Hassas Irani , Sergiy A. Vorobyov , Yongwei Huang

Stochastic Optimization (SO) is a classical approach for optimization under uncertainty that typically requires knowledge about the probability distribution of uncertain parameters. As the latter is often unknown, Distributionally Robust…

The effects of treatments are often heterogeneous, depending on the observable characteristics, and it is necessary to exploit such heterogeneity to devise individualized treatment rules (ITRs). Existing estimation methods of such ITRs…

Econometrics · Economics 2022-08-09 Daido Kido

Federated learning (FL) enables collaborative model training without direct data sharing, but its performance can degrade significantly in the presence of data distribution perturbations. Distributionally robust optimization (DRO) provides…

Machine Learning · Computer Science 2025-09-30 Zifan Wang , Xinlei Yi , Xenia Konti , Michael M. Zavlanos , Karl H. Johansson

Established approaches to obtain generalization bounds in data-driven optimization and machine learning mostly build on solutions from empirical risk minimization (ERM), which depend crucially on the functional complexity of the hypothesis…

Optimization and Control · Mathematics 2022-10-14 Yibo Zeng , Henry Lam

Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called…

Optimization and Control · Mathematics 2025-06-30 Yufeng Yang , Yi Zhou , Zhaosong Lu

Graphs are playing a crucial role in different fields since they are powerful tools to unveil intrinsic relationships among signals. In many scenarios, an accurate graph structure representing signals is not available at all and that…

Machine Learning · Computer Science 2021-05-14 Xiang Zhang , Yinfei Xu , Qinghe Liu , Zhicheng Liu , Jian Lu , Qiao Wang

We consider a minimax problem motivated by distributionally robust optimization (DRO) when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization…

Machine Learning · Statistics 2024-12-31 Linglingzhi Zhu , Yao Xie

We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…

Optimization and Control · Mathematics 2026-05-27 Zusen Xu , Jia-Jie Zhu

We review distributionally robust optimization (DRO), a principled approach for constructing statistical estimators that hedge against the impact of deviations in the expected loss between the training and deployment environments. Many…

Methodology · Statistics 2024-01-29 Jose Blanchet , Jiajin Li , Sirui Lin , Xuhui Zhang

One key challenge for multi-task Reinforcement learning (RL) in practice is the absence of task indicators. Robust RL has been applied to deal with task ambiguity, but may result in over-conservative policies. To balance the worst-case…

Machine Learning · Computer Science 2022-10-25 Mengdi Xu , Peide Huang , Yaru Niu , Visak Kumar , Jielin Qiu , Chao Fang , Kuan-Hui Lee , Xuewei Qi , Henry Lam , Bo Li , Ding Zhao

Wasserstein distance-based distributionally robust optimization (DRO) has received much attention lately due to its ability to provide a robustness interpretation of various learning models. Moreover, many of the DRO problems that arise in…

Optimization and Control · Mathematics 2019-10-29 Jiajin Li , Sen Huang , Anthony Man-Cho So

Several applications of Reinforcement Learning suffer from instability due to high variance. This is especially prevalent in high dimensional domains. Regularization is a commonly used technique in machine learning to reduce variance, at…

Machine Learning · Computer Science 2019-04-12 Pierre Thodoroff , Audrey Durand , Joelle Pineau , Doina Precup