  By exploiting ultrafast and irregular time series generated by lasers with
delayed feedback, we have previously demonstrated a scalable algorithm to solve
multi-armed bandit (MAB) problems utilizing the time-division multiplexing of
laser chaos time series. Although the algorithm detects the arm with the
highest reward expectation, the correct recognition of the order of arms in
terms of reward expectations is not achievable. Here, we present an algorithm
where the degree of exploration is adaptively controlled based on confidence
intervals that represent the estimation accuracy of reward expectations. We
have demonstrated numerically that our approach did improve arm order
recognition accuracy significantly, along with reduced dependence on reward
environments, and the total reward is almost maintained compared with
conventional MAB methods. This study applies to sectors where the order
information is critical, such as efficient allocation of resources in
information and communications technology.
