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Risk-sensitive safety analysis using Conditional Value-at-Risk

Abstract : This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risksensitive safe sets as sub-level sets of the solution to a non-standard 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 under-approximations 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 under-approximations 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
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Submitted on : Monday, December 6, 2021 - 2:12:13 PM
Last modification on : Tuesday, January 4, 2022 - 6:21:14 AM

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Margaret Chapman, Riccardo Bonalli, Kevin Smith, Insoon Yang, Marco Pavone, et al.. Risk-sensitive safety analysis using Conditional Value-at-Risk. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2021, pp.1-1. ⟨10.1109/TAC.2021.3131149⟩. ⟨hal-03467256⟩

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