Efficient importance sampling schemes for a feed-forward network

Abstract

The aim of this article is to construct efficient importance sampling schemes for a rare event, namely, the buffer overflow associated with a feed-forward network with discontinuous dynamics. This is done through a piecewise constant change of measure, which is based on a suitably constructed subsolution to an HJB equation. The main task is to change the measure such that the logarithmic asymptotic optimality is achieved. To that end, we find an upper bound on the second moment of the importance sampling estimator that yields optimality. Numerical simulations illustrate the validity of theoretical results.