Efficient Uncertainty Propagation with Guarantees in Wasserstein Distance

2025/06/10 by Eduardo Figueiredo, Figueiredo, Eduardo, Steven Adams +5 · 1 citation
Computer Science · Decision Sciences · #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Risk and Portfolio Optimization #Stochastic Gradient Optimization Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2506.08689

openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 set of distributions close in the Wasserstein distance, we compute a set of distributions centered at a discrete distribution that is guaranteed to contain the pushforward of any distribution in the input set. Our approach is based on approximating a nominal distribution from the input set to a discrete support distribution for which the exact computation of the pushforward distribution is tractable, thus guaranteeing computational efficiency to our approach. Then, we rely on results from semi-discrete optimal transport and distributional robust optimization to show that for any ε> 0 the error introduced by our approach can be made smaller than ε. Critically, in the context of dynamical systems, we show how our results allow one to efficiently approximate the distribution of a stochastic dynamical system with a discrete support distribution for a possibly infinite horizon while bounding the resulting approximation error. We empirically investigate the effectiveness of our framework on various benchmarks, including a 10-D non-linear system, showing the effectiveness of our approach in quantifying uncertainty in linear and non-linear stochastic systems.

Citations

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Cited by

• discretize_distributions: Efficient Quantization of Gaussian Mixtures with Guarantees in Wasserstein Distance

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