Mobile crowdsensing is a powerful mechanism to aggregate hyper-local knowledge about the environment. Indeed, users may contribute valuable observations across time and space using the sensors embedded in their smartphones. However, the relevance of the provided measurements depends on the adequacy of the sensing context with respect to the phenomena that are analyzed. This paper concentrates more specifically on assessing the sensing context when gathering observations about the physical environment beyond its geographical position in the Euclidean space, i.e., whether the phone is in-/out-pocket, in-/out-door and on-/under-ground. We introduce an online learning approach to the local inference of the sensing context so as to overcome the disparity of the classification performance due to the heterogeneity of the sensing devices as well as the diversity of user behavior and novel usage scenarios. Our approach specifically features a hierarchical algorithm for inference that requires few opportunistic feedbacks from the user, while increasing the accuracy of the context inference per user.