Learning-based importance sampling via stochastic optimal control for stochastic reaction networks

Abstract We explore efficient estimation of statistical quantities, particularly rare event probabilities, for stochastic reaction networks. Consequently, we propose an importance sampling (IS) approach to improve the Monte Carlo (MC) estimator efficiency based on approximate tau-leap scheme. The crucial step in IS framework is choosing appropriate change probability measure achieve substantial variance reduction. This task typically challenging and often requires insights into underlying problem. Therefore, automated obtain a highly path-dependent original connection network context between finding optimal parameters within class measures control formulation. Optimal are obtained by solving minimization First, derive associated dynamic programming equation. Analytically this backward equation challenging, hence formulation find near-optimal parameters. To mitigate curse dimensionality, learning-based method value function using neural network, where determined via optimization algorithm. Our analysis numerical experiments verify that proposed substantially reduces MC variance, resulting lower computational complexity regime, compared with standard estimators.