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

Margaret P Chapman (1) , Riccardo Bonalli (2) , Kevin M Smith (3) , Insoon Yang (4) , Marco Pavone (5) , Claire J Tomlin (6)

1 DCS - Department of Computer Science [University of Toronto]
2 L2S - Laboratoire des signaux et systèmes
3 Tufts University [Medford]
4 Department of Electrical and Computer Engineering [Seoul National University]
5 Stanford University
6 EECS - Department of Electrical Engineering and Computer Science [Berkeley]

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

Domaines: Optimisation et contrôle [math.OC]

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