Wasserstein Distributionally Robust Rare-Event Simulation

TL;DR

This paper introduces a new distributionally robust importance sampling method for rare-event probability estimation under distributional uncertainty, achieving vanishing relative error and outperforming existing methods.

Contribution

We develop DRIS, a novel, computationally efficient importance sampling technique that provides distributionally robust bounds and guarantees vanishing relative error in rare-event simulation.

Findings

DRIS achieves vanishing relative error in rare-event probability estimation.

Numerical studies show DRIS outperforms existing benchmarks.

The method is simple to implement with low sampling costs.

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.