In numerous settings, agents lack sufficient data to learn a model directly. Collaborating with other agents may help, but introduces a bias-variance trade-off when local data distributions differ. A key challenge is for each agent to identify clients with similar distributions while learning the model, a problem that remains largely unresolved. This study focuses on a particular instance of the overarching problem, where each agent collects samples from a real-valued distribution over time to estimate its mean. Existing algorithms face impractical per-agent space and time complexities (linear in the number of agents |A|). To address scalability challenges, we propose a framework where agents self-organize into a graph, allowing each agent to communicate with only a selected number of peers r. We propose two collaborative mean estimation algorithms: one employs a consensus-based approach, while the other uses a message-passing scheme, with complexity O(r) and O(r log |A|), respectively. We establish conditions for both algorithms to yield asymptotically optimal estimates and we provide a theoretical characterization of their performance.

The advent of Large Language Models (LLMs) and generative AI is fundamentally transforming information retrieval and processing on the Internet, bringing both great potential and significant concerns regarding content authenticity and reliability.This paper presents a novel quantitative approach to shed light on the complex information dynamics arising from the growing use of generative AI tools.Despite their significant impact on the digital ecosystem, these dynamics remain largely uncharted and poorly understood.We propose a stochastic model to characterize the generation, indexing, and dissemination of information in response to new topics.This scenario particularly challenges current LLMs, which often rely on real-time Retrieval-Augmented Generation (RAG) techniques to overcome their static knowledge limitations.Our findings suggest that the rapid pace of generative AI adoption, combined with increasing user reliance, can outpace human verification, escalating the risk of inaccurate information proliferation across digital resources.An in-depth analysis of Stack Exchange data confirms that high-quality answers inevitably require substantial time and human effort to emerge.This underscores the considerable risks associated with generating persuasive text in response to new questions and highlights the critical need for responsible development and deployment of future generative AI tools.