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In this paper we explore the use of symbolic knowledge and machine teaching to reduce human data labeling efforts in building neural task bots. We propose SYNERGY, a hybrid learning framework where a task bot is developed in two steps: (i) Symbolic knowledge to neural networks: Large amounts of simulated dialog sessions are generated based on task-specific symbolic knowledge which is represented as a task schema consisting of dialog flows and task-oriented databases. Then a pre-trained neural dialog model, SOLOIST, is fine-tuned on the simulated dialogs to build a bot for the task. (ii) Neural learning: The fine-tuned neural dialog model is continually refined with a handful of real task-specific dialogs via machine teaching, where training samples are generated by human teachers interacting with the task bot. We validate SYNERGY on four dialog tasks. Experimental results show that SYNERGY maps task-specific knowledge into neural dialog models achieving greater diversity and coverage of dialog flows, and continually improves model performance with machine teaching, thus demonstrating strong synergistic effects of symbolic knowledge and machine teaching.