  Motivated by the increasing adoption of models which facilitate greater
automation in risk management and decision-making, this paper presents a novel
Importance Sampling (IS) scheme for measuring distribution tails of objectives
modelled with enabling tools such as feature-based decision rules, mixed
integer linear programs, deep neural networks, etc. Conventional efficient IS
approaches suffer from feasibility and scalability concerns due to the need to
intricately tailor the sampler to the underlying probability distribution and
the objective. This challenge is overcome in the proposed black-box scheme by
automating the selection of an effective IS distribution with a transformation
that implicitly learns and replicates the concentration properties observed in
less rare samples. This novel approach is guided by a large deviations
principle that brings out the phenomenon of self-similarity of optimal IS
distributions. The proposed sampler is the first to attain asymptotically
optimal variance reduction across a spectrum of multivariate distributions
despite being oblivious to the underlying structure. The large deviations
principle additionally results in new distribution tail asymptotics capable of
yielding operational insights. The applicability is illustrated by considering
product distribution networks and portfolio credit risk models informed by
neural networks as examples.
