Wasserstein Distributionally Robust Rare-Event Simulation

2026-01-04

AI Summary

This work addresses the significant performance degradation of standard rare-event simulation methods under distributional uncertainty. To overcome this limitation, the authors propose a Distributionally Robust Importance Sampling (DRIS) framework that characterizes ambiguity in the underlying probability distribution using a Wasserstein ambiguity set. By leveraging duality theory, the method constructs an estimator that is robust to the worst-case distribution within this set. Notably, DRIS is the first approach to achieve vanishing relative error guarantees in distributionally robust rare-event simulation, simultaneously ensuring high estimation accuracy while substantially reducing variance and sampling cost. Numerical experiments demonstrate that DRIS markedly outperforms existing benchmark methods in both estimation accuracy and computational efficiency.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event probabilities subject to such distributional model risk. Specifically, we focus on computing worst-case rare-event probabilities, defined as a distributionally robust bound against a Wasserstein ambiguity set centered at a specific nominal distribution. By exploiting a dual characterization of this bound, we propose Distributionally Robust Importance Sampling (DRIS), a computationally tractable methodology designed to substantially reduce the variance associated with estimating the dual components. The proposed method is simple to implement and requires low sampling costs. Most importantly, it achieves vanishing relative error, the strongest efficiency guarantee that is notoriously difficult to establish in rare-event simulation. Our numerical studies confirm the superior performance of DRIS against existing benchmarks.

Problem

• rare-event simulation
• distributional uncertainty
• Wasserstein ambiguity set
• distributionally robust optimization
• model risk

Innovation

• Wasserstein distributionally robust
• rare-event simulation
• importance sampling
• vanishing relative error
• ambiguity set