Learning from a Mixture of Information Sources

2026-09-27

AI Summary

This study investigates how the distribution of information sources affects decision-makers' learning efficiency, contrasting source-aware and source-blind observation modes. Building upon an extension of the Blackwell experiment model, we employ mean-preserving spread analysis and a repeated-sampling learning framework to reveal how signal source distributions shape information value. Our results demonstrate that source-aware decision-makers exhibit risk-seeking preferences over information sources, whereas the learning performance of source-blind agents remains unaffected by the spread of the source distribution. Furthermore, provided the average signal is not completely uninformative, source-blind agents require only an O(1/ε) multiplicative increase in sample size to match the learning efficacy of their source-aware counterparts. This work quantifies the efficiency gap between these two modes, offering a theoretical foundation for understanding information value and data requirement boundaries under varying observational conditions.

Abstract

We often learn from multiple sources that convey information in different ways. How informative is it to know the source of a signal, and how is this informativeness shaped by the distribution of sources? We extend the standard (binary-state, binary-signal) Blackwell experiment model by introducing a commonly known distribution over signaling schemes, representing the distribution of information sources. We compare learning under two information models: source-aware, where decision makers observe a signaling scheme and its realization (e.g., raw reviews, search results), and source-blind, where only the signal realization is observed (e.g., aggregate ratings, LLM-generated summaries). We show that a mean-preserving spread in the distribution of signaling schemes translates into Blackwell dominance for source-aware decision makers, implying they are"risk-loving"in information sources. In contrast, it has no impact on source-blind decision makers. When learning from repeated draws of signaling schemes, source-blind decision makers learn more slowly. However, as long as the average signaling scheme is $\varepsilon$ away from being completely uninformative, source-blind learning can match source-aware learning by using at most $O(1/\varepsilon)$ times more data.

Problem

• information sources
• Blackwell experiment
• source-aware learning
• source-blind learning
• signaling schemes

Innovation

• Blackwell experiment
• information sources
• source-aware learning
• source-blind learning
• mean-preserving spread