# Autocorrelation effects in a stochastic-process model for solving two-armed bandit problems

arXiv: https://arxiv.org/abs/2603.05559 · HTML: https://mlsanity.com/paper/2603.05559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 44 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [Photonics for artificial intelligence and neuromorphic computing](https://mlsanity.com/paper/2011.00111/) (2020)
- [Ultrafast photonic reinforcement learning based on laser chaos](https://mlsanity.com/paper/1704.04379/) (2017)
- [Efficient Decision-Making by Volume-Conserving Physical Object](https://mlsanity.com/paper/1412.6141/) (2014)
- [Scalable photonic reinforcement learning by time-division multiplexing of laser chaos](https://mlsanity.com/paper/1803.09425/) (2018)
- [Dynamic channel selection in wireless communications via a multi-armed bandit algorithm using laser chaos time series](https://mlsanity.com/paper/1909.03629/) (2019)
- [Controlling chaotic itinerancy in laser dynamics for reinforcement learning](https://mlsanity.com/paper/2205.05987/) (2022)
- [Adaptive model selection in photonic reservoir computing by reinforcement learning](https://mlsanity.com/paper/2004.12575/) (2020)
- [Parallel photonic accelerator for decision making using optical spatiotemporal chaos](https://mlsanity.com/paper/2210.06976/) (2022)
- [Theory of Acceleration of Decision Making by Correlated Time Sequences](https://mlsanity.com/paper/2203.16004/) (2022)
- [Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk](https://mlsanity.com/paper/2304.10118/) (2023)
- [A study of the Antlion Random Walk](https://mlsanity.com/paper/2503.12775/) (2025)

## Abstract (arXiv)

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 for solving the two-armed bandit problem based on time series, 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 one, whereas positive autocorrelation is useful when the sum of the winning probabilities is less than one. Moreover, the performance is independent of autocorrelation if the sum of the winning probabilities equals one, which is mathematically clarified. This study paves the way for solving the two-armed bandit problems for reinforcement learning applications in wireless communications and robotics.