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Moral outrage shapes fundamental aspects of human 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 pre-registered observational studies of Twitter (7,331 users and 12.7 million total tweets) and two pre-registered 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. We also find that outrage expressions are sensitive to expressive norms in users’ social networks, over and above users’ own preferences, suggesting that norm learning processes guide online outrage expressions. Moreover, expressive norms moderate social reinforcement of outrage: 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 impact moral discourse in digital public spaces.