Joint Inference of Reward Machines and Policies for Reinforcement Learning

  • Zhe Xu The University of Texas at Austin
  • Ivan Gavran Max Planck Institute for Software Systems
  • Yousef Ahmad University of Texas at Austin
  • Rupak Majumdar Max Planck Institute for Software Systems
  • Daniel Neider Max Planck Institute for Software Systems
  • Ufuk Topcu The University of Texas at Austin
  • Bo Wu The University of Texas at Austin


Incorporating high-level knowledge is an effective way to expedite reinforcement learning (RL), especially for complex tasks with sparse rewards. We investigate an RL problem where the high-level knowledge is in the form of reward machines, a type of Mealy machines that encode non-Markovian reward functions. We focus on a setting in which this knowledge is a priori not available to the learning agent. We develop an iterative algorithm that performs joint inference of reward machines and policies for RL (more specifically, q-learning). In each iteration, the algorithm maintains a hypothesis reward machine and a sample of RL episodes. It uses a separate q-function defined for each state of the current hypothesis reward machine to determine the policy and performs RL to update the q-functions. While performing RL, the algorithm updates the sample by adding RL episodes along which the obtained rewards are inconsistent with the rewards based on the current hypothesis reward machine. In the next iteration, the algorithm infers a new hypothesis reward machine from the updated sample. Based on an equivalence relation between states of reward machines, we transfer the q-functions between the hypothesis reward machines in consecutive iterations. We prove that the proposed algorithm converges almost surely to an optimal policy in the limit. The experiments show that learning high-level knowledge in the form of reward machines leads to fast convergence to optimal policies in RL, while the baseline RL methods fail to converge to optimal policies after a substantial number of training steps.