Infants’ remarkable learning abilities allow them to rapidly acquire many complex skills. It has been suggested that infants achieve this learning by optimally allocating their attention to relevant stimuli in the environment, but the underlying mechanisms remain poorly understood. Here, we modeled infants’ looking behavior during a learning task through an ideal learner that quantified the informational structure of environmental stimuli. We show that saccadic latencies, looking time, and time spent engaged with a stimulus sequence are explained by the properties of the learning environments, including the level of surprise of the stimulus, overall predictability of the environment, and progress in learning the environmental structure. These findings reveal the factors that shape infants’ advanced learning, emphasizing their predisposition to seek out stimuli that maximize learning.