Teaching and learning in uncertainty

We investigate a simple model for social learning with two agents: a teacher and a student. The teacher's goal is to teach the student the state of the world Θ, however, the teacher herself is not certain about Θ and needs to simultaneously learn it and teach it to the student. We model the teacher's and the student's uncertainty via binary symmetric channels, and employ a simple heuristic decoder at the student's end. We focus on two teaching strategies: a "low effort" strategy of simply forwarding information, and a "high effort" strategy of communicating the teacher's current best estimate of Θ at each time instant. Using tools from large deviation theory, we calculate the exact learning rates for these strategies and demonstrate regimes where the low effort strategy outperforms the high effort strategy. Our primary technical contribution is a detailed analysis of the large deviation properties of the sign of a transient Markov random walk on ℤ.