We consider long-lived agents who interact repeatedly in a social network. In each period, each agent learns about an unknown state by observing a private signal and her neighbors’ actions from the previous period before choosing her own action. Our main result shows that the learning rate of the slowest-learning agent is bounded from above by a constant that only depends on the marginal distributions of the agents’ private signals and not on the number of agents, the network structure, correlations between the private signals, and 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 general conditions. This extends recent findings on equilibrium learning and demonstrates that the limitation stems from an information-theoretic tradeoff between optimal action choices and information revelation, rather than strategic considerations. We also show that a social planner can achieve almost optimal learning by designing strategies for which each agent’s learning rate is close to the upper bound.