Theory of Acceleration of Decision Making by Correlated Time Sequences

TL;DR

This paper presents a theoretical model explaining how negatively correlated ultrafast laser chaos accelerates decision-making in multi-armed bandit problems, supported by analytical and simulation results.

Contribution

It introduces a unified theoretical framework linking correlated time series to decision-making acceleration, validated by analytical and numerical comparisons.

Findings

Negative autocorrelation improves decision-making performance.

The theoretical model aligns with numerical simulations.

Optimal system design can be achieved based on the model.

Abstract

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.