Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method

TL;DR

This paper introduces an optimized nested simulation design that efficiently allocates inner replications across fixed outer scenarios using the likelihood ratio method, reducing total simulation effort while maintaining accuracy.

Contribution

It proposes a novel bi-level optimization approach for nested simulation with fixed outer scenarios, leveraging likelihood ratio pooling to improve efficiency.

Findings

Achieves (\u03b3^{-1})$ mean squared error with given budget.

Outperforms regression-based pooling methods in numerical tests.

Provides asymptotic convergence analysis of the estimator.

Abstract

In nested simulation literature, a common assumption is that the experimenter can choose the number of outer scenarios to sample. This paper considers the case when the experimenter is given a fixed set of outer scenarios from an external entity. We propose a nested simulation experiment design that pools inner replications from one scenario to estimate another scenario's conditional mean via the likelihood ratio method. Given the outer scenarios, we decide how many inner replications to run at each outer scenario as well as how to pool the inner replications by solving a bi-level optimization problem that minimizes the total simulation effort. We provide asymptotic analyses on the convergence rates of the performance measure estimators computed from the optimized experiment design. Under some assumptions, the optimized design achieves $\cO(\Gamma^{-1})$ mean squared error of the estimators given simulation budget $\Gamma$. Numerical experiments demonstrate that our design outperforms a state-of-the-art design that pools replications via regression.