Risk-Sensitive Safety Analysis Using Conditional Value-at-Risk

This article develops a safetyanalysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sublevel sets solution nonstandard optimal control problem, where random maximum cost assessed via Conditional Value-at-Risk (CVaR). The objective function represents extent constraint violation state trajectory, averaged over given percentage worst cases. problem well-motivated but difficult solve tractably because temporal decomposition CVaR history-dependent. Our primary theoretical contribution derive computationally tractable underapproximations risk-sensitive sets. provides novel, theoretically guaranteed, parameter-dependent upper bound without need augment space. For fixed parameter value, only one Markov decision process required obtain any family risk-sensitivity levels. In addition, we propose second definition provide their estimation using bound. expressed in terms new coherent risk functional, which inspired by CVaR. demonstrate our numerical examples.