CVaR-based Safety Analysis in the Infinite Time Horizon Setting

TL;DR

This paper introduces a risk-averse safety analysis approach for stochastic systems over infinite horizons, using CVaR to measure worst-case severity, with theoretical guarantees and a stormwater management example.

Contribution

It presents a novel CVaR-based safety analysis framework for infinite horizon stochastic systems, including theoretical conditions for optimal policy existence.

Findings

The method effectively quantifies risk in worst-case scenarios.

The value iteration algorithm converges under certain conditions.

Numerical example demonstrates practical applicability.

Abstract

We develop a risk-averse safety analysis method for stochastic systems on discrete infinite time horizons. Our method quantifies the notion of risk for a control system in terms of the severity of a harmful random outcome in a fraction of the worst cases. In contrast, classical methods quantify risk in terms of the probability of a harmful event. Our theoretical arguments are based on the analysis of a value iteration algorithm on an augmented state space. We provide conditions to guarantee the existence of an optimal policy on this space. We illustrate the method numerically using an example from the domain of stormwater management.