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For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
This paper presents an extension of Naor's analysis on the join-or-balk problem in observable M/M/1 queues. While all other Markovian assumptions still hold, we explore this problem assuming uncertain arrival rates under the…
Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning combating distributional uncertainty, e.g., the uncertainty of an empirical distribution compared…
We study a methodology to tackle the NASA Langley Uncertainty Quantification Challenge problem, based on an integration of robust optimization, more specifically a recent line of research known as distributionally robust optimization, and…
This paper addresses a novel \emph{cost-sensitive} distributionally robust log-optimal portfolio problem, where the investor faces \emph{ambiguous} return distributions, and a general convex transaction cost model is incorporated. The…
Knowledge of the underlying causal relations is essential for inferring the effect of interventions in complex systems. In a widely studied approach, structural causal models postulate noisy functional relations among interacting variables,…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach…
We propose a distributionally robust logistic regression model with an unfairness penalty that prevents discrimination with respect to sensitive attributes such as gender or ethnicity. This model is equivalent to a tractable convex…
In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…
Reinforcement learning (RL) policies often fail under dynamics that differ from training, a gap not fully addressed by domain randomization or existing adversarial RL methods. Distributionally robust RL provides a formal remedy but still…
In this paper, we focus on a data-driven risk-averse multistage stochastic programming (RMSP) model considering distributional robustness. We optimize the RMSP over the worst-case distribution within an ambiguity set of probability…
Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization…
We study distributionally robust Expected Shortfall when the distribution of the underlying is perturbed by a size quantified with optimal transport distance based on the quadratic cost function. In the dual version of the robust…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules…
Adversarial risk quantifies the performance of classifiers on adversarially perturbed data. Numerous definitions of adversarial risk -- not all mathematically rigorous and differing subtly in the details -- have appeared in the literature.…
Safety assurance is uncompromisable for safety-critical environments with the presence of drastic model uncertainties (e.g., distributional shift), especially with humans in the loop. However, incorporating uncertainty in safe learning will…