Efficient Black-Box Importance Sampling for VaR and CVaR Estimation

This paper considers efficient Importance Sampling (IS) for the estimation of tail risks of a loss defined in terms of a sophisticated object such as a machine learning predictor or a mixed-integer linear optimization formulation. Assuming only black-box access to the loss and the distribution of the underlying random vector, the paper presents an efficient IS algorithm for estimating the Value at Risk and Conditional Value at Risk. The key challenge in any IS procedure, namely, identifying an appropriate change-of-measure, is automated with a self-structuring IS transformation that learns and replicates the concentration properties of the conditional excess from less rare samples. The resulting estimators are enjoy asymptotically optimal variance reduction when viewed in the logarithmic scale. Simulation experiments, both on synthetic and real datasets, highlight the efficacy and practicality of the proposed IS scheme.