Autocorrelation effects in a stochastic-process model for decision making via time series
arXiv:2603.05559v1 Announce Type: new Abstract: Decision makers exploiting photonic chaotic dynamics obtained by semiconductor lasers provide an ultrafast approach to solving multi-armed bandit problems by using a temporal optical signal as the driving source for sequential decisions. In such systems, the sampling interval of the chaotic waveform shapes the temporal correlation of the resulting time series, and experiments have reported that decision accuracy depends strongly on this autocorrelation property. However, it remains unclear whether the benefit of autocorrelation can be explained by a minimal mathematical model. Here, we analyze a stochastic-process model of the time-series-based decision making using the tug-of-war principle for solving the two-armed bandit problem, where the threshold and a two-valued Markov signal evolve jointly. Numerical results reveal an environment-dependent structure: negative (positive) autocorrelation is optimal in reward-rich (reward-poor) envir
arXiv:2603.05559v1 Announce Type: new Abstract: Decision makers exploiting photonic chaotic dynamics obtained by semiconductor lasers provide an ultrafast approach to solving multi-armed bandit problems by using a temporal optical signal as the driving source for sequential decisions. In such systems, the sampling interval of the chaotic waveform shapes the temporal correlation of the resulting time series, and experiments have reported that decision accuracy depends strongly on this autocorrelation property. However, it remains unclear whether the benefit of autocorrelation can be explained by a minimal mathematical model. Here, we analyze a stochastic-process model of the time-series-based decision making using the tug-of-war principle for solving the two-armed bandit problem, where the threshold and a two-valued Markov signal evolve jointly. Numerical results reveal an environment-dependent structure: negative (positive) autocorrelation is optimal in reward-rich (reward-poor) environments. These findings show that negative autocorrelation of the time series is advantageous when the sum of the winning probabilities is more than $1$, whereas positive autocorrelation is useful when the sum of the winning probabilities is less than $1$. Moreover, the performance is independent of autocorrelation if the sum of the winning probabilities equals $1$, which is mathematically clarified. This study paves the way for improving the decision-making scheme for reinforcement learning applications in wireless communications and robotics.
Executive Summary
This study investigates the impact of autocorrelation on decision-making processes in time-series-based systems. Using a stochastic-process model of the two-armed bandit problem, the authors demonstrate that autocorrelation affects decision accuracy in a manner dependent on the environment. Specifically, negative autocorrelation is optimal in reward-rich environments, while positive autocorrelation is beneficial in reward-poor environments. Notably, the study reveals that performance is independent of autocorrelation when the sum of winning probabilities equals 1. These findings have significant implications for reinforcement learning applications in wireless communications and robotics.
Key Points
- ▸ Autocorrelation significantly impacts decision-making accuracy in time-series-based systems.
- ▸ The optimal autocorrelation depends on the environment, with negative autocorrelation preferred in reward-rich environments and positive autocorrelation in reward-poor environments.
- ▸ Performance is independent of autocorrelation when the sum of winning probabilities equals 1.
Merits
Strength
The study provides a comprehensive mathematical analysis of autocorrelation effects on decision-making processes, offering valuable insights for reinforcement learning applications.
Demerits
Limitation
The study assumes a simplified two-armed bandit problem, which may not accurately represent real-world decision-making scenarios.
Expert Commentary
This study represents a significant contribution to the field of reinforcement learning, as it provides a comprehensive mathematical analysis of autocorrelation effects on decision-making processes. The findings have important implications for the development of more efficient time-series analysis techniques, which can be applied to a wide range of real-world decision-making scenarios. However, the study's limitations, such as its assumption of a simplified two-armed bandit problem, should be considered in the context of more complex decision-making scenarios. Nevertheless, the study's results offer valuable insights for the development of more effective decision-making algorithms and policies in various fields.
Recommendations
- ✓ Future studies should investigate the application of the study's findings to more complex decision-making scenarios, such as multi-armed bandit problems and real-world decision-making domains.
- ✓ Researchers should explore the development of more efficient time-series analysis techniques that take into account the autocorrelation effects demonstrated in this study.
