Related papers: Wasserstein Two-Sided Chance Constraints with An A…
We propose an open loop control scheme for linear systems with time-varying random elements in the plant's state matrix. This paper focuses on joint chance constraints for potentially time-varying target sets. Under assumption of finite and…
We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for…
We consider synthesis and analysis of probability measures using the entropy-regularized Wasserstein-2 cost and its unbiased version, the Sinkhorn divergence. The synthesis problem consists of computing the barycenter, with respect to these…
The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…
Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…
This paper is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and…
This paper investigates advantages of using 2-Wasserstein ambiguity sets over 1-Wasserstein sets in two-stage distributionally robust optimization with right-hand side uncertainty. We examine the worst-case distributions within 1- and…
Keeping the balance between supply and demand is a fundamental task in power system operational planning practices. This task becomes particularly challenging due to the deepening penetration of renewable energy resources, which induces a…
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…
We suggest that the tools of contraction analysis for deterministic systems can be applied towards studying the convergence behavior of stochastic dynamical systems in the Wasserstein metric. In particular, we consider the case of Ito…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
In this paper, we consider contextual stochastic optimization problems under endogenous uncertainty, where decisions affect the underlying distributions. To implement such decisions in practice, it is crucial to ensure that their outcomes…
We consider the rate-distortion function for lossy source compression, as well as the channel capacity for error correction, through the lens of distributional robustness. We assume that the distribution of the source or of the additive…
We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein discrepancies to the empirical distribution. Using the notion…
Autonomous vehicles face the problem of optimizing the expected performance of subsequent maneuvers while bounding the risk of collision with surrounding dynamic obstacles. These obstacles, such as agent vehicles, often exhibit stochastic…
We examine the infinite-dimensional optimization problem of finding a decomposition of a probability measure into K probability sub-measures to minimize specific loss functions inspired by applications in clustering and user grouping. We…
We investigate an expected utility maximization problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model $\mathbb{P}$ with an adverse choice from a Wasserstein ball of…
Uncertainty modeling has become increasingly important in power system decision-making. The widely-used tractable uncertainty modeling method-chance constraints with Conditional Value at Risk (CVaR) approximation, can be overconservative…
Policy optimization is a core component of reinforcement learning (RL), and most existing RL methods directly optimize parameters of a policy based on maximizing the expected total reward, or its surrogate. Though often achieving…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…