The E ect of Representation and Knowledge on Goal-Directed Exploration with Reinforcement-Learning Algorithms: The Proofs

The article proves that the algorithms are tractable with only a simple change in the reward structure (\penalizing the agent for action executions") or in the initialization of the values that they maintain, and proves properties of admissible Qor Q̂-learning in deterministic state spaces if the initial Q-values are consistent.