Abstract: How do people decide whether it is worth pursuing innovation? For example, in machine learning new methods often result from combining existing methods, but there is a risk that a given combination will not work. While seasoned experts could use their intuitions gained through experience to decide whether some combinations are worth trying out, novices to the field have to learn these insights while trying to maximize their rewards. Here, we formalize this problem and derive optimal policies for agents who know, or do not know, how likely each kind of combination is to succeed, emulating the effects of expert knowledge. Our model predicts that novices should not only gather fewer rewards, but also explore systematically less than the experts. An online behavioral experiment ($n=300$) supports this finding, showcasing the profound impact of domain expertise in guiding innovative decision making in a combinatorial space.