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

• 成果类型: Article
• 署名作者: Chapman, Margaret P.; Bonalli, Riccardo; Smith, Kevin M.; Yang, Insoon; Pavone, Marco; Tomlin, Claire J.
• 署名单位: University of Toronto; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Tufts University; Seoul National University (SNU); Stanford University; University of California System; University of California Berkeley
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3131149
• 发表日期: 2022
• 页码: 6521-6536
• 关键词: Conditional value-at-risk (CVaR); Markov decision processes (MDPs); safety analysis; stochastic optimal control

摘要

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