Related papers: Sinkhorn Distributionally Robust Optimization
We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a…
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or…
We study distributionally robust online learning, where a risk-averse learner updates decisions sequentially to guard against worst-case distributions drawn from a Wasserstein ambiguity set centered at past observations. While this paradigm…
In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we…
Motivated by the Bures distance, we introduce a new family of distances, \emph{relative translation invariant Wasserstein distances}, denoted by $RW_p$, as an extension of the classical Wasserstein distances $W_p$ for $p \in [1, +\infty)$.…
Entropic regularization provides a simple way to approximate linear programs whose constraints split into two or more tractable blocks. The resulting objectives are amenable to cyclic Kullback-Leibler (KL) Bregman projections, with…
In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
Using the recently developed Sinkhorn algorithm for approximating the Wasserstein distance between probability distributions represented by Monte Carlo samples, we demonstrate exponential filter stability of two commonly used nonlinear…
Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially…
This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
In this paper, we investigate distributionally robust model order reduction for linear, discrete-time, time-invariant systems. The external input is assumed to follow an uncertain distribution within a Wasserstein ambiguity set. We begin by…
We study a model for adversarial classification based on distributionally robust chance constraints. We show that under Wasserstein ambiguity, the model aims to minimize the conditional value-at-risk of the distance to misclassification,…
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…
Many problems in machine learning can be formulated as solving entropy-regularized optimal transport on the space of probability measures. The canonical approach involves the Sinkhorn iterates, renowned for their rich mathematical…
This paper focuses on solving a data-driven distributionally robust optimization problem over a network of agents. The agents aim to minimize the worst-case expected cost computed over a Wasserstein ambiguity set that is centered at the…
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…
We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local…