  Photonic accelerators have been intensively studied to provide enhanced
information processing capability to benefit from the unique attributes of
physical processes. Recently, it has been reported that chaotically oscillating
ultrafast time series from a laser, called laser chaos, provide the ability to
solve multi-armed bandit (MAB) problems or decision-making problems at GHz
order. Furthermore, it has been confirmed that the negatively correlated
time-domain structure of laser chaos contributes to the acceleration of
decision-making. However, the underlying mechanism of why decision-making is
accelerated by correlated time series is unknown. In this study, we demonstrate
a theoretical model to account for accelerating decision-making by correlated
time sequence. We first confirm the effectiveness of the negative
autocorrelation inherent in time series for solving two-armed bandit problems
using Fourier transform surrogate methods. We propose a theoretical model that
concerns the correlated time series subjected to the decision-making system and
the internal status of the system therein in a unified manner, inspired by
correlated random walks. We demonstrate that the performance derived
analytically by the theory agrees well with the numerical simulations, which
confirms the validity of the proposed model and leads to optimal system design.
The present study paves the way for improving the effectiveness of correlated
time series for decision-making, impacting artificial intelligence and other
applications.
