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Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
This paper proposes a distributionally robust approach to regret optimal control of discrete-time linear dynamical systems with quadratic costs subject to a stochastic additive disturbance on the state process. The underlying probability…
In this paper, we propose a minimax linear-quadratic control method to address the issue of inaccurate distribution information in practical stochastic systems. To construct a control policy that is robust against errors in an empirical…
The two-sample homogeneity testing problem is fundamental in statistics and becomes particularly challenging in high dimensions, where classical tests can suffer substantial power loss. We develop a learning-assisted procedure based on the…
Over the past years, the share of electricity production from wind power plants has increased to significant levels in several power systems across Europe and the United States. In order to cope with the fluctuating and partially…
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…
Distributed consensus in the Wasserstein metric space of probability measures on the real line is introduced in this work. Convergence of each agent's measure to a common measure is proven under a weak network connectivity condition. The…
We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we…
Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…
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…
We present a novel $Q$-learning algorithm tailored to solve distributionally robust Markov decision problems where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
We study a generalized distributionally robust chance-constrained set covering problem (DRC) with a Wasserstein ambiguity set, where both decisions and uncertainty are binary-valued. We establish the NP-hardness of DRC and recast it as a…
Motivated by approximation Bayesian computation using mean-field variational approximation and the computation of equilibrium in multi-species systems with cross-interaction, this paper investigates the composite geodesically convex…