Related papers: Bayesian distributionally robust variational inequ…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
We introduce a new framework, Bayesian Distributionally Robust Optimization (Bayesian-DRO), for data-driven stochastic optimization where the underlying distribution is unknown. Bayesian-DRO contrasts with most of the existing DRO…
Inspired by the recent work by Shapiro et al. [45], we propose a Bayesian distributionally robust Nash equilibrium (BDRNE) model where each player lacks complete information on the true probability distribution of the underlying uncertainty…
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…
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 introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…
We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…
This paper is concerned with the approximation of probability distributions known up to normalization constants, with a focus on Bayesian inference for large-scale inverse problems in scientific computing. In this context, key challenges…
Decision making under uncertainty is challenging since the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs about the model's parameters. However, minimising the…
This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…
Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…
The study of robustness has received much attention due to its inevitability in data-driven settings where many systems face uncertainty. One such example of concern is Bayesian Optimization (BO), where uncertainty is multi-faceted, yet…
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…
We study stochastic Nash equilibrium problems subject to heterogeneous uncertainty on the expected valued cost functions of the individual agents, where we assume no prior knowledge of the underlying probability distributions of the…
In this work, we develop a novel data-driven Bayesian nonparametric Wasserstein distributionally robust optimization (BNWDRO) framework for decision-making under uncertainty. The proposed framework unifies a Bayesian nonparametric method…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
Nash Equilibrium and its robust counterpart, Distributionally Robust Nash Equilibrium (DRNE), are fundamental problems in game theory with applications in economics, engineering, and machine learning. This paper addresses the problem of…
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…
We develop variational regularization methods which leverage sparsity-promoting priors to solve severely ill posed inverse problems defined on the 3D ball (i.e. the solid sphere). Our method solves the problem natively on the ball and thus…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…