Related papers: Don't Look Back in Anger: Wasserstein Distribution…
Transfer learning is a popular strategy to leverage external knowledge and improve statistical efficiency, particularly with a limited target sample. We propose a novel knowledge-guided Wasserstein Distributionally Robust Optimization…
This paper investigates two optimal insurance contracting problems under distributional uncertainty from the perspective of a potential policyholder, utilizing a Bregman-Wasserstein (BW) ball to characterize the ambiguity set of loss…
Structuring ambiguity sets in Wasserstein-based distributionally robust optimization (DRO) can improve their statistical properties when the uncertainty consists of multiple independent components. The aim of this paper is to solve…
This paper presents a framework for Wasserstein distributionally robust (DR) regret-optimal (RO) control in the context of partially observable systems. DR-RO control considers the regret in LQR cost between a causal and non-causal…
Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…
We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the…
We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…
We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
Wasserstein barycenter, built on the theory of optimal transport, provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it…
Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for…
A new data-enabled control technique for uncertain linear time-invariant systems, recently conceived by Coulson et\ al., builds upon the direct optimization of controllers over input/output pairs drawn from a large dataset. We adopt an…
This paper studies data-driven distributionally robust bottleneck combinatorial problems (DRBCP) with stochastic costs, where the probability distribution of the cost vector is contained in a ball of distributions centered at the empirical…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
Wasserstein distributionally robust control (WDRC) is an effective method for addressing inaccurate distribution information about disturbances in stochastic systems. It provides various salient features, such as an out-of-sample…
To address the issue of inaccurate distributions in practical stochastic systems, a minimax linear-quadratic control method is proposed using the Wasserstein metric. Our method aims to construct a control policy that is robust against…
We consider probabilistic models for sequential observations which exhibit gradual transitions among a finite number of states. We are particularly motivated by applications such as human activity analysis where observed accelerometer time…
We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…
In this paper, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…