Groupe d’études et de recherche en analyse des décisions

Risk-sensitive safety analysis via conditional value-at-risk

Margaret P. Chapman University of Toronto, Canada

Margaret P. Chapman

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Risk-sensitive safety analysis is a safety analysis method for stochastic systems on Borel spaces that uses a risk functional from finance called Conditional Value-at-Risk (CVaR). CVaR provides a particularly expressive way to quantify the safety of a control system, as it represents the average cost in a fraction of worst cases. We define the notion of a risk-sensitive safe set in terms of a non-standard optimal control problem, in which a maximum cost is assessed via CVaR. We present a method to compute risk-sensitive safe sets exactly in principle by utilizing a state-space augmentation technique, and we provide a measurable selection condition to guarantee the existence of an optimal pre-commitment policy. The proposed framework assumes continuous system dynamics and cost functions but is otherwise flexible. In particular, it can accommodate probabilistic control policies, fairly general disturbance distributions, and control-dependent, non-monotonic, and non-convex stage costs. In addition, we present a method to compute under-approximations to risk-sensitive safe sets, which substantially improves computational tractability. We demonstrate how risk-sensitive safety analysis is useful for a stormwater infrastructure application. Our numerical examples are inspired by current challenges that cities face in managing precipitation uncertainty.

Biography: Margaret Chapman is an Assistant Professor in the Department of Electrical and Computer Engineering at the University of Toronto, which she joined in July 2020. Her research focuses on risk-sensitive and stochastic control, with emphasis on safety analysis and applications in healthcare and sustainable cities. She earned her BS degree with Distinction and MS degree in Mechanical Engineering from Stanford University in 2012 and 2014, respectively. Margaret earned her PhD degree in Electrical Engineering and Computer Sciences from the University of California Berkeley (UC Berkeley) in August 2020. In 2021, Margaret received a Leon O. Chua Award for outstanding achievement in nonlinear science from her doctoral alma mater. In addition, she is a recipient of a US National Science Foundation Graduate Research Fellowship, Berkeley Fellowship for Graduate Study, a Fulbright Scholarship (granted by the US Department of State), and a Stanford University Terman Engineering Scholastic Award.