We consider long-lived agents who interact repeatedly in a social network. In each period, each agent observes a private signal, chooses an action, and then observes the actions of her neighbors. We show that the learning rate of the slowest-learning agent is capped by a constant that depends only on the distribution of the most informative private signal, but not on the number of agents, the network structure, correlations between the private signals, or the agents’ strategies. Applying this result to equilibrium learning with rational agents shows that the learning rate of all agents in any equilibrium is bounded under a broad class of conditions. The result is driven by an information-theoretic tradeoff between optimal action choices and information revelation.