Achieving Efficiency in Black Box Simulation of Distribution Tails with Self-structuring Importance Samplers
This work addresses a bottleneck in simulation-based estimation for practitioners in fields like finance and operations research, offering a broadly applicable solution.
The paper tackles the challenge of efficiently estimating distribution tails in complex models by introducing a novel Importance Sampling scheme that overcomes the feasibility and scalability issues of conventional methods, achieving asymptotically optimal variance reduction across multivariate distributions without requiring model-specific tuning.
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