We propose an interactive-predictive neural machine translation framework for easier model personalization using reinforcement and imitation learning. During the interactive translation process, the user is asked for feedback on uncertain locations identified by the system. Responses are weak feedback in the form of "keep" and "delete" edits, and expert demonstrations in the form of "substitute" edits. Conditioning on the collected feedback, the system creates alternative translations via constrained beam search. In simulation experiments on two language pairs our systems get close to the performance of supervised training with much less human effort.