Human Activity Recognition (HAR) is an important research issue for pervasive computing that aims to identify human activities in smart homes. In the literature, most reasoning approaches for HAR are based on centralized approach where a central system is responsible for processing and reasoning about sensor data in order to recognize activities. Since sensor data are distributed, heterogeneous, and dynamic (i.e., whose characteristics are varying over time) in the smart home, reasoning process on these data for HAR needs to be distributed over a group of heterogeneous, autonomous and interacting entities in order to be more efficient. This paper proposes a main contribution, the DCR approach, a fully Distributed Collaborative Reasoning multi-agent approach where agents, with diverse classifiers, observe sensor data, make local predictions, communicate and collaborate to identify current activities. Then, an improved version of the DCR approach is proposed, the DCR-OL approach, a distributed Online Learning approach where learning agents learns from their collaborations to improve their own performance in activity recognition. Finally, we test our approaches by performing an evaluation study on Aruba dataset, that indicates an enhancement in terms of accuracy, F-measure and G-mean metrics compared to the centralized approach and also compared to a distributed approach existing in the literature.