Theory of Acceleration of Decision Making by Correlated Time Sequences
This work provides a theoretical foundation for optimizing decision-making systems using correlated time series, potentially impacting artificial intelligence applications, though it is incremental as it builds on prior experimental findings.
The authors tackled the problem of understanding why correlated time sequences accelerate decision-making in multi-armed bandit problems, and they developed a theoretical model that analytically explains this acceleration and agrees with numerical simulations.
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.