When Machine Learning Meets Importance Sampling: A More Efficient Rare Event Estimation Approach

Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be inefficient, due to the exploding variance of the path-dependent likelihood functions. To mitigate this, we introduce a new importance sampling approach that utilizes a marginal likelihood ratio on the stationary distribution, effectively avoiding the issue of excessive variance. In addition, we design a machine learning algorithm to estimate this marginal likelihood ratio using importance sampling data. Numerical experiments indicate that our algorithm outperforms the classic importance sampling methods.