Offline Contextual Learning with Correlated Bayesian Beliefs

In this work, we investigate the offline contextual learning in simulation optimization. In offline contextual learning, the optimal design changes with the context. Therefore, the optimal design needs to be carefully determined for each possible context. Existing research has paid little attention to the impact of correlations between different designs’ performances on the efficiency of offline contextual learning. In this study, we consider the Bayesian framework and utilize a multi-output Gaussian process to capture correlations between different designs’ performances. We verify that considering correlations can accelerate the decay of posterior variance. Taking the KG-type strategy as an example, we construct a new Bayesian sampling policy, CIKG. Finally, we show the effectiveness of CIKG through numerical experiments.