Interacting Stochastic Systems with Agent-Based Sampling and Connection-Based Reinforcement
Abstract
We introduce a general class of interacting reinforced stochastic systems evolving on a network. The dynamics are governed by two distinct interaction structures: a sampling network, which determines how information is acquired, and a reinforcement network, which determines how the sampled information influences future evolution. Processes generate Bernoulli observations through preferential, de-preferential, or mixed sampling, while observations are transmitted through an edge-dependent affine reinforcement mechanism. We formulate the dynamics as a stochastic approximation scheme and study their asymptotic behaviour. We establish sufficient conditions for almost sure convergence to a deterministic limit and, when the sampling and reinforcement graphs coincide, derive graph-theoretic criteria involving odd cycles, mixed-sampling vertices, and subcritical reinforcement. Under additional structural assumptions, we establish almost sure convergence and partial synchronization in a random-limit regime. In the deterministic regime, we also prove a law of the iterated logarithm and a central limit theorem under suitable spectral and regularity conditions. Finally, we show how the framework encompasses interacting urn models with edge-dependent reinforcement, urns with memory, and random walks with memory.
Related
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BibTeX
@misc{dahiya2026interacting,
title = {{Interacting Stochastic Systems with Agent-Based Sampling and Connection-Based Reinforcement}},
author = {Yogesh Dahiya and Gursharn Kaur and Neeraja Sahasrabudhe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13884},
eprint = {2610.13884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13884},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interacting Stochastic Systems with Agent-Based Sampling and Connection-Based Reinforcement
AU - Yogesh Dahiya
AU - Gursharn Kaur
AU - Neeraja Sahasrabudhe
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13884
UR - https://arxiv.org/abs/2610.13884
AB - We introduce a general class of interacting reinforced stochastic systems evolving on a network. The dynamics are governed by two distinct interaction structures: a sampling network, which determines how information is acquired, and a reinforcement network, which determines how the sampled information influences future evolution. Processes generate Bernoulli observations through preferential, de-preferential, or mixed sampling, while observations are transmitted through an edge-dependent affine reinforcement mechanism. We formulate the dynamics as a stochastic approximation scheme and study their asymptotic behaviour. We establish sufficient conditions for almost sure convergence to a deterministic limit and, when the sampling and reinforcement graphs coincide, derive graph-theoretic criteria involving odd cycles, mixed-sampling vertices, and subcritical reinforcement. Under additional structural assumptions, we establish almost sure convergence and partial synchronization in a random-limit regime. In the deterministic regime, we also prove a law of the iterated logarithm and a central limit theorem under suitable spectral and regularity conditions. Finally, we show how the framework encompasses interacting urn models with edge-dependent reinforcement, urns with memory, and random walks with memory.
ER -