Dynamic Choice of Information Sources

An agent learns in continuous time from two information sources, each associated with a hypothesis. If a hypothesis is true, the associated source confirms it at a positive rate. False hypotheses are never confirmed. The agent's optimal learning strategy has two phases. During the first phase, the agent follows his beliefs; that is, at each moment, he learns from the source associated with the most likely hypothesis according to his current beliefs. During the second phase, he follows the opposite rule and focuses on the least likely hypothesis