How would you search for a unique, fashionable shoe that a friend wore and you want to buy, but you didn't take a picture? Existing approaches propose interactive image search as a promising venue. However, they either entrust the user with taking the initiative to provide informative feedback, or give all control to the system which determines informative questions to ask. Instead, we propose a mixed-initiative framework where both the user and system can be active participants, depending on whose initiative will be more beneficial for obtaining high-quality search results. We develop a reinforcement learning approach which dynamically decides which of three interaction opportunities to give to the user: drawing a sketch, providing free-form attribute feedback, or answering attribute-based questions. By allowing these three options, our system optimizes both the informativeness and exploration capabilities allowing faster image retrieval. We outperform three baselines on three datasets and extensive experimental settings.