  This paper presents a novel Importance Sampling (IS) scheme for estimating
distribution tails of performance measures modeled with a rich set of tools
such as linear programs, integer linear programs, piecewise linear/quadratic
objectives, feature maps specified with deep neural networks, etc. The
conventional approach of explicitly identifying efficient changes of measure
suffers from feasibility and scalability concerns beyond highly stylized
models, due to their need to be tailored intricately to the objective and the
underlying probability distribution. This bottleneck is overcome in the
proposed scheme with an elementary transformation which is capable of
implicitly inducing an effective IS distribution in a variety of models by
replicating the concentration properties observed in less rare samples. This
novel approach is guided by developing 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
specifics of the underlying model. Its applicability is illustrated with
contextual shortest path and portfolio credit risk models informed by neural
networks
