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

翻译：本文提出了一种新颖的重要性采样（IS）方案，用于估计性能测度的分布尾部，这些测度可通过丰富的工具集建模，如线性规划、整数线性规划、分段线性/二次目标函数、深度神经网络指定的特征映射等。传统方法通过显式识别测度的高效变化来操作，但除了高度简化的模型外，该方法面临可行性和可扩展性问题，因为它需要根据目标和底层概率分布进行精细定制。所提出的方案通过一种基本变换克服了这一瓶颈，该变换通过复制在较少罕见样本中观察到的集中性质，能够隐式地在多种模型中诱导出有效的IS分布。这一新颖方法基于大偏差原理的发展，揭示了最优IS分布的自相似现象。所提出的采样器是首个在无视底层模型具体细节的情况下，在多元分布族中实现渐近最优方差缩减的采样器。其适用性通过神经网络驱动的上下文最短路径和组合信用风险模型进行了说明。