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We are motivated by the real challenges presented in a human-robot system to develop new designs that are efficient at data level and with performance guarantees such as stability and optimality at systems level. Existing approximate/adaptive dynamic programming (ADP) results that consider system performance theoretically are not readily providing practically useful learning control algorithms for this problem; and reinforcement learning (RL) algorithms that address the issue of data efficiency usually do not have performance guarantees for the controlled system. This study fills these important voids by introducing innovative features to the policy iteration algorithm. We introduce flexible policy iteration (FPI), which can flexibly and organically integrate experience replay and supplemental values from prior experience into the RL controller. We show system level performances including convergence of the approximate value function, (sub)optimality of the solution, and stability of the system. We demonstrate the effectiveness of the FPI via realistic simulations of the human-robot system. It is noted that the problem we face in this study may be difficult to address by design methods based on classical control theory as it is nearly impossible to obtain a customized mathematical model of a human-robot system either online or offline. The results we have obtained also indicate the great potential of RL control to solving realistic and challenging problems with high dimensional control inputs.