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We introduce the notion of Worst-Case Sensitivity, defined as the worst-case rate of increase in the expected cost of a Distributionally Robust Optimization (DRO) model when the size of the uncertainty set vanishes. We show that worst-case…

In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…

We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…

We consider a two-stage distributionally robust optimization (DRO) model with multimodal uncertainty, where both the mode probabilities and uncertainty distributions could be affected by the first-stage decisions. To address this setting,…

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…

This paper introduces a novel framework for assessing risk and decision-making in the presence of uncertainty, the \emph{$\varphi$-Divergence Quadrangle}. This approach expands upon the traditional Risk Quadrangle, a model that quantifies…

In this paper, we refine and generalize closed forms for worst-case law invariant convex risk measures with uncertainty sets based on: i) closed balls under $p$-norms and Wasserstein distance; and ii) moment constraints involving mean and…

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…

Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome…

The Wasserstein distance between mixing measures has come to occupy a central place in the statistical analysis of mixture models. This work proposes a new canonical interpretation of this distance and provides tools to perform inference on…

Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…

Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…

Computer vision systems that are deployed in safety-critical applications need to quantify their output uncertainty. We study regression from images to parameter values and here it is common to detect uncertainty by predicting probability…

In this paper, we discuss the ambiguous chance constrained based portfolio optimization problems, in which the perturbations associated with the input parameters are stochastic in nature, but their distributions are not known precisely. We…

Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…

In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a…

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…

We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this…