Anticipating the learning consequences of actions is crucial to plan efficient information seeking. Such a capacity is needed for learners to determine which actions are most likely to result in learning. Here, we tested the early ontogeny of the human capacity to anticipate the amount of learning gained from seeing. In study 1, we tested infants' capacity to anticipate the availability of sight. Fourteen-month-old infants (N = 72) were invited to search for a toy hidden inside a container. The participants were faster to attempt at opening a shutter when this action allowed them to see inside the container. Moreover, this effect was specifically observed when seeing inside the container was potentially useful to the participants' goals. Thus, infants anticipated the availability of sight, and they calibrated their information-seeking behaviors accordingly. In studies 2 and 3, we tested toddlers' capacity to anticipate whether data would be cognitively useful for their goals. Two-and-a-half-year-olds (N = 72) had to locate a target character hidden among distractors. The participants flipped the characters more often, and were comparatively faster to initiate this action when it yielded access to visual data allowing them to locate the target. Thus, toddlers planned their information-seeking behaviors by anticipating the cognitive utility of sight. In contrast, toddlers did not calibrate their behaviors to the cognitive usefulness of auditory data. These results suggest that cognitive models of learning guide toddlers' search for information. The early developmental onset of the capacity to anticipate future learning gains is crucial for active learning.