Discourse structures provide a way to extract deep semantic information from text, e.g., about relations conveying causal and temporal information and topical organization, which can be gainfully employed in NLP tasks such as summarization, document classification, sentiment analysis. But the task of automatically learning discourse structures is difficult: the relations that make up the structures are very sparse relative to the number of possible semantic connections that could be made between any two segments within a text; furthermore, the existence of a relation between two segments depends not only on “local” features of the segments, but also on “global” contextual information, including which relations have already been instantiated in the text and where. It is natural to try to leverage the power of deep learning methods to learn the complex representations discourse structures require. However, deep learning methods demand a large amount of labeled data, which becomes prohibitively expensive in the case of expertly-annotated discourse corpora. One recent advance in the resolution of this “training data bottleneck”, data programming, allows for the implementation of expert knowledge in weak supervision system for data labeling. In this article, we present the results of our application of the data programming paradigm to the problem of discourse structure learning for multi-party dialogues.