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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2503.12775 |
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| _version_ | 1866917055984304128 |
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| author | Narimatsu, Akihiro Yamagami, Tomoki |
| author_facet | Narimatsu, Akihiro Yamagami, Tomoki |
| contents | Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor lasers to solve multi-armed bandit (MAB) problems at ultrafast speeds, and its threshold adjustment mechanism has been modeled as an RW. However, previous analyses assumed complete memory preservation ($α= 1$), overlooking the role of partial memory in balancing exploration and exploitation. In this paper, we introduce the Antlion Random Walk (ARW), defined by $X_t = αX_{t-1} + ξ_t$ with $α\in [0,1]$ and Rademacher-distributed increments $(ξ_t)$, which describes a walker pulled back toward the origin before each step. We show that varying $α$ significantly alters ARW dynamics, yielding distributions that range from uniform-like to normal-like. Through mathematical and numerical analyses, we investigate expectation, variance, reachability, positive-side residence time, and distributional similarity. Our results place ARWs within the framework of autoregressive (AR(1)) processes while highlighting distinct non-Gaussian features, thereby offering new theoretical insights into memory-aware stochastic modeling of decision-making systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A study of the Antlion Random Walk Narimatsu, Akihiro Yamagami, Tomoki Probability Logic in Computer Science 60E05, 68Q87 Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor lasers to solve multi-armed bandit (MAB) problems at ultrafast speeds, and its threshold adjustment mechanism has been modeled as an RW. However, previous analyses assumed complete memory preservation ($α= 1$), overlooking the role of partial memory in balancing exploration and exploitation. In this paper, we introduce the Antlion Random Walk (ARW), defined by $X_t = αX_{t-1} + ξ_t$ with $α\in [0,1]$ and Rademacher-distributed increments $(ξ_t)$, which describes a walker pulled back toward the origin before each step. We show that varying $α$ significantly alters ARW dynamics, yielding distributions that range from uniform-like to normal-like. Through mathematical and numerical analyses, we investigate expectation, variance, reachability, positive-side residence time, and distributional similarity. Our results place ARWs within the framework of autoregressive (AR(1)) processes while highlighting distinct non-Gaussian features, thereby offering new theoretical insights into memory-aware stochastic modeling of decision-making systems. |
| title | A study of the Antlion Random Walk |
| topic | Probability Logic in Computer Science 60E05, 68Q87 |
| url | https://arxiv.org/abs/2503.12775 |