A Hybrid of Shrinking Ball Method and Optimal Large Deviation Rate Estimation in Continuous Contextual Simulation Optimization with Single Observation

We propose a new method for solving continuous contextual simulation optimization with a single observation. By adopting the estimation on the large deviation rate in the contextual ranking and selection problem, we transfer the old theorem to the continuous setting using a shrinking ball inspired construct. Through the estimation of the rate, the new method is expected to achieve the optimal performance in this new problem setting. Brief numerical experiments are conducted and show significant advantages of our method against the uniform sampling scheme.