The Sample Complexity of Teaching by Reinforcement on Q-Learning


  • Xuezhou Zhang University of Wisconsin-Madison
  • Shubham Bharti University of Wisconsin-Madison
  • Yuzhe Ma University of Wisconsin-Madison
  • Adish Singla MPI-SWS
  • Xiaojin Zhu University of Wisconsin-Madison


Reinforcement Learning


We study the sample complexity of teaching, termed as ``teaching dimension" (TDim) in the literature, for the teaching-by-reinforcement paradigm, where the teacher guides the student through rewards. This is distinct from the teaching-by-demonstration paradigm motivated by robotics applications, where the teacher teaches by providing demonstrations of state/action trajectories. The teaching-by-reinforcement paradigm applies to a wider range of real-world settings where a demonstration is inconvenient, but has not been studied systematically. In this paper, we focus on a specific family of reinforcement learning algorithms, Q-learning, and characterize the TDim under different teachers with varying control power over the environment, and present matching optimal teaching algorithms. Our TDim results provide the minimum number of samples needed for reinforcement learning, and we discuss their connections to standard PAC-style RL sample complexity and teaching-by-demonstration sample complexity results. Our teaching algorithms have the potential to speed up RL agent learning in applications where a helpful teacher is available.




How to Cite

Zhang, X., Bharti, S., Ma, Y., Singla, A., & Zhu, X. (2021). The Sample Complexity of Teaching by Reinforcement on Q-Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 35(12), 10939-10947. Retrieved from



AAAI Technical Track on Machine Learning V