Risk-Sensitive Safety Analysis Using Conditional Value-at-Risk
Risk-Sensitive Safety Analysis Using Conditional Value-at-Risk
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DOI：
10.1109/tac.2021.3131149
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发表时间：
2021-01
影响因子：
6.8
通讯作者：
Margaret P. Chapman;Riccardo Bonalli;K. Smith;Insoon Yang;M. Pavone;C. Tomlin
中科院分区：
文献类型：
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作者：
Margaret P. Chapman;Riccardo Bonalli;K. Smith;Insoon Yang;M. Pavone;C. Tomlin
本文提出了一种随机系统的安全分析方法，该方法对罕见的有害结果的可能性和严重性敏感。我们将风险敏感安全集定义为非标准最优控制问题解的子水平集，其中通过条件风险价值（CVaR）评估随机最大成本。目标函数表示状态轨迹的约束违反的最大程度，在给定百分比的最坏情况下平均。这个问题是有动机的，但难以解决，因为CVaR的时间分解是历史依赖的。我们的主要理论贡献是获得计算上易于处理的下近似风险敏感的安全集。我们的方法提供了一个新的，理论上保证，参数依赖的上限CVaR的最大成本，而不需要增加状态空间。对于一个固定的参数值，只需要一个马尔可夫决策过程问题的解决方案，以获得任何家庭的风险敏感性水平的下近似。此外，我们提出了风险敏感的安全集的第二个定义，并提供了一个易于处理的方法来估计，而不使用参数依赖的上限。第二个定义是一个新的一致的风险功能，这是受CVaR的启发。我们证明了我们的主要理论贡献，通过数值例子。
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.