Abstract: Since collecting and annotating data for spatio-temporal action detection is very expensive, there is a need to learn approaches with less supervision. Weakly supervised approaches do not require any bounding box annotations and can be trained only from labels that indicate whether an action occurs in a video clip. Current approaches, however, cannot handle the case when there are multiple persons in a video that perform multiple actions at the same time. In this work, we address this very challenging task for the first time. We propose a baseline based on multi-instance and multi-label learning. Furthermore, we propose a novel approach that uses sets of actions as representation instead of modeling individual action classes. Since computing the probabilities for the full power set becomes intractable as the number of action classes increases, we assign an action set to each detected person under the constraint that the assignment is consistent with the annotation of the video clip. We evaluate the proposed approach on the challenging AVA dataset where the proposed approach outperforms the MIML baseline and is competitive to fully supervised approaches.