When deciding whether to explore, people must consider both their need for information, and the cost of obtaining it.Thus, to judge why someone explores (or decides not to), we must consider not only their actions, but also the cost ofinformation. Do children attend to the cost of agents exploratory choices when inferring what others know or desireto know? In Experiment 1, four- and five-year-olds judged that an agent who rejected an opportunity to gain low-costinformation must have already known it. In Experiment 2, four- and five-year-olds judged that an agent who incurreda greater cost to gain information had a greater epistemic desire. In two control experiments, we show that these resultscannot be explained by a low-level heuristic linking competence with knowledge. Our results suggest that childrens Theoryof Mind includes expectations about how costs interact with epistemic desires to produce action.

Functional relations are prevalent in everyday life and science. Do children have intuitive knowledge of functional relations, and can they learn these relations by active information gathering (i.e., choosing a few input values and observing the corresponding outputs)? We found that 6- to 9-year-olds can learn different families of functions (linear, Gaussian, and exponential) through both informative data provided by an experimenter and data they gather from the environment for themselves. Overall, children learn linear functions more accurately than non-linear functions. When choosing data points to learn about, some children select highly similar points that only shed light on a narrow region of a function, while others choose more variable inputs and gain a more holistic view of a function. Children who use this latter, globally informative strategy have higher learning accuracy, particularly for non-linear functions. Results suggest that children are in the process of developing effective strategies for active function learning.

We investigate people’s use of strategies for sampling data in an active learning task. In the spirit of resource-rational analysis, we argue that people may often use effective heuristics to guide sampling in lieu of more computationally expensive optimization strategies, but that when they encounter evidence that their heuristics are now ineffective they flexibly shift to new strategies. When the function family changed, participants quickly updated their beliefs about the likely function family on subsequent trials. By clustering participants’ sampling behaviour, we show that people can employ varied sampling strategies, shifting strategies more often when encountering unusual function families that are more adversarial to generic sampling strategies. Not all new strategies improved participants’ performance on a subsequent prediction task; nonetheless, people’s ability to dynamically shift their active learning behaviour may help them understand the abstract features of complex relationships.

When deciding how to act in new situations, we expect agents todraw on relevant prior experiences. This expectation underliesmany of our mental-state inferences, allowing us to infer agents’prior knowledge from their current actions. Do children sharethis expectation, and use it to infer others’ epistemic states? InExperiment 1, we find that five- and six-year-olds (but not four-year-olds) attribute additional knowledge to agents whose priorexperiences cannot explain their success. In Experiment 2, wefind that six-year-olds (but not younger children) also attributegreater knowledge to agents whose prior experience cannotexplain their failure. We show that by age five or six, childrenexpect ignorant agents’ beliefs (and therefore their actions) to beguided by their prior knowledge. This work adds to a growingbody of research suggesting that, while infants can representmental states, the ability to infer mental states continues todevelop throughout early childhood.