Evolution of Information in Interactive Decision Making: A Case Study for Multi-Armed Bandits

Yuzhou Gu (Massachusetts Institute of Technology) · Yanjun Han (New York University) · Jian Qian (Massachusetts Institute of Technology)
behavioral differencescharacterizing performancedecouplingfixed margingrowth phasesinformation evolutioninformation gaininteractive decision makinglearning dynamicsmutual informationnon-interactive environmentsoptimal armoptimal learningstochastic multi-armed banditsuccess probability

We study the evolution of information in interactive decision making through the lens of a stochastic multi-armed bandit problem. Focusing on a fundamental example where a unique optimal arm outperforms the rest by a fixed margin, we characterize the optimal success probability and mutual information over time. Our findings reveal distinct growth phases in mutual information