On Optimizing the Conditional Value-at-Risk of a Maximum Cost for Risk-Averse Safety Analysis

The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider nonstandard optimal problem which goal is minimize CVaR maximum random cost subject Borel-space Markov decision process. objective represents departure desired operating region averaged over given fraction worst cases. This provides safety criterion for stochastic system that informed by both probability xmlns:xlink="http://www.w3.org/1999/xlink">severity potential consequences system’s behavior. In contrast, existing analysis frameworks apply stagewise constraints or assess probability constraint violation without quantifying severity violation. To best our knowledge, interest not solved. solve problem, we propose study family dynamic programs on an augmented state space. prove enjoys equivalent representation terms solutions these under appropriate assumptions. For each program, show existence policy depends dynamics numerical example, illustrate how framework useful assessing combined sewer overflows precipitation uncertainty.