相关论文: A new local time-decoupled squared Wasserstein-2 m…

We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein information geometry. It defines a parametrization invariant…

When training the parameters of a linear dynamical model, the gradient descent algorithm is likely to fail to converge if the squared-error loss is used as the training loss function. Restricting the parameter space to a smaller subset and…

Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…

We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…

We propose a distributionally robust data-driven predictive control framework for stochastic linear time-invariant systems with unknown dynamics and disturbance distributions. We use an offline trajectory to fit the subspace predictive…

In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for paramerizations. We present a…

While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

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,…

Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown…

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…

Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…

In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a…

Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…

In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…

We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances…

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis…

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and…