Neural Network-Assisted Simulation Optimization with Covariates

In real-time decision-making problems for complicated stochastic systems, a covariate that reflects the state of the system is observed in real time and a state-dependent decision needs to be made immediately to optimize some system performance. Such system performances, for complicated stochastic systems, often are not in closed-form and require time-consuming simulation experiments to evaluate, which can be prohibitive in real-time tasks. We propose two neural network-assisted methods to address this challenge by effectively utilizing simulation experiments that are conducted offline before the real-time tasks. One key step in the proposed methods integrates a classical simulation meta-modelling approach with neural networks to jointly capture the mapping from the covariate and the decision variable to the system performance, which enhances the use of offline simulation data and reduces the risk of model misspecification. A brief numerical experiment is presented to illustrate the performance of the proposed methods.