Moral outrage shapes fundamental aspects of social life and is now widespread in online social networks. Here, we show how social learning processes amplify online moral outrage expressions over time. In two preregistered observational studies on Twitter (7331 users and 12.7 million total tweets) and two preregistered behavioral experiments (N = 240), we find that positive social feedback for outrage expressions increases the likelihood of future outrage expressions, consistent with principles of reinforcement learning. In addition, users conform their outrage expressions to the expressive norms of their social networks, suggesting norm learning also guides online outrage expressions. Norm learning overshadows reinforcement learning when normative information is readily observable: in ideologically extreme networks, where outrage expression is more common, users are less sensitive to social feedback when deciding whether to express outrage. Our findings highlight how platform design interacts with human learning mechanisms to affect moral discourse in digital public spaces.