We examine how a human-robot interaction (HRI) system may be designed when input-output data from previous experiments are available. In particular, we consider how to select an optimal impedance in the assistance design for a cooperative manipulation task with a new operator. Due to the variability between individuals, the design parameters that best suit one operator of the robot may not be the best parameters for another one. However, by incorporating historical data using a linear auto-regressive (AR-1) Gaussian process, the search for a new operator's optimal parameters can be accelerated. We lay out a framework for optimizing the human-robot cooperative manipulation that only requires input-output data. We establish how the AR-1 model improves the bound on the regret and numerically simulate a human-robot cooperative manipulation task to show the regret improvement. Further, we show how our approach's input-output nature provides robustness against modeling error through an additional numerical study.