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

doi:10.1109/TAC.2021.3131149

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

2022-12-01

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Margaret P. Chapman *

DOI：10.1109/TAC.2021.3131149

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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.

Keywords:

Conditional Value-at-Risk (CVaR)

Markov decision processes (MDPs)

safety analysis

stochastic optimal control

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

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