On the Expressivity of Markov Reward (Extended Abstract)

On the Expressivity of Markov Reward (Extended Abstract)

David Abel, Will Dabney, Anna Harutyunyan, Mark K. Ho, Michael L. Littman, Doina Precup, Satinder Singh

Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence
Sister Conferences Best Papers. Pages 5254-5258. https://doi.org/10.24963/ijcai.2022/730

Reward is the driving force for reinforcement-learning agents. We here set out to understand the expressivity of Markov reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of "task": (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to perform each task type, and correctly determine when no such reward function exists.
Keywords:
Artificial Intelligence: General