NeurIPS 2020

PAC-Bayesian Bound for the Conditional Value at Risk

Meta Review

Conditional Value at Risk or Expected Shortfall (CVaR) of a random variable is the expected value of this random variable conditionally on the fact that this random variable exceeds a given value. As example, it quantifies the amount of tail risk an investment portfolio has. This kind of value is of importance in many situations and is getting more attention in the ML community. Indeed, a learned predictor that has a bad accuracy might nevertheless be of high utility if it get some a high CVaR provided there is a particular interest for examples that are in the best quantile (e.g., best drivers for a car insurance compagnies ... the only ones that should qualify for a reduction of their insurance quotes. There is still a lot to understand on CVaR from the learning theory point of view, this paper proposes the first known PAC-Bayesian bound for CVaR. This results has to be shared with the NeurIPS community.