This academic paper, published in the journal Games and Economic Behavior, discusses the possibility of Bayesian learning in infinitely repeated games. The author examines prior research suggesting limitations on rational learning in such games, particularly the difficulty of achieving both belief consistency and strategy learnability. The paper proposes a modified concept called "optimizing learnability," which focuses on the ability of players to learn optimal strategies rather than any possible strategy. The author argues that this redefined notion of learnability, when combined with ε-consistency, is sufficient for convergence to approximate Nash equilibrium, even in a broader class of games than previously thought possible. The text includes formal definitions, lemmas, and a theorem to support its claims, along with examples illustrating the application of the theory in coordination games.