High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems

This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with quantifiable probability and can be exploited to formulate robust stochastic optimization problems with out...

Distributionally Robust Strategy Synthesis for Switched Stochastic Systems

We present a novel framework for formal control of uncertain discrete-time switched stochastic systems against probabilistic reach-avoid specifications. In particular, we consider stochastic systems with additive noise, whose distribution lies in an ambiguity set of distributions that are ε−close to a nominal one according to the Wasserstein...

Comparing structured ambiguity sets for stochastic optimization: Application to uncertainty quantification

The aim of this paper is to compare two classes of structured ambiguity sets, which are data-driven and can reduce the conservativeness of their associated optimization problems. These two classes of structured sets, coined Wasserstein hyperrectangles and multi-transport hyperrectangles, are explored in their trade-offs in terms of reducing...

Data-Driven Distributionally Robust Coverage Control by Mobile Robots

This paper provides a data-driven solution to the problem of coverage control by which a team of robots aims to optimally deploy in a spatial region where certain event of interest may occur. This event is random and described by a probability density function, which is unknown and can only be learned by collecting data. In this work, we...

Uncertain uncertainty in data-driven stochastic optimization: towards structured ambiguity sets

Ambiguity sets of probability distributions are a prominent tool to hedge against distributional uncertainty in stochastic optimization. The aim of this paper is to build tight Wasserstein ambiguity sets for data-driven optimization problems. The method exploits independence between the distribution components to introduce structure in the...

Distributionally Robust Optimization via Haar Wavelet Ambiguity Sets

This paper introduces a spectral parameterization of ambiguity sets to hedge against distributional uncertainty in stochastic optimization problems. We build an ambiguity set of probability densities around a histogram estimator, which is constructed by independent samples from the unknown distribution. The densities in the ambiguity set are...