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How do people actively explore to learn about functional rules, that is, how continuous inputs map onto continuous outputs? We introduce a novel paradigm to investigate information search in continuous, multi-feature function learning scenarios. Participants either actively selected or passively observed information to learn about an underlying linear function. We develop and compare different variants of rule-based (linear regression) and non-parametric (Gaussian process regression) active learning approaches to model participants' active learning behavior. Our results show that participants' performance is best described by a rule-based model that attempts to efficiently learn linear functions with a focus on high and uncertain outcomes. These results advance our understanding of how people actively search for information to learn about functional relations in the environment.

Changing one variable at a time while controlling others is a key aspect of scientific experimentation and a central component of STEM curricula. However, children reportedly struggle to learn and implement this strategy. Why do children’s intuitions about how best to intervene on a causal system conflict with scientific practices? Mathematical analyses have shown that controlling variables is not always the most efficient learning strategy, and that its effectiveness depends on the “causal sparsity” of the problem, i.e., how many variables are likely to impact the outcome. We tested the degree to which 7- to 13-year-old children (n = 104) adapt their learning strategies based on expectations about causal sparsity. We report new evidence demonstrating that some previous work may have undersold children’s causal learning skills: Children can perform and interpret controlled experiments, are sensitive to causal sparsity, and use this information to tailor their testing strategies, demonstrating adaptive decision-making.