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Oral
On the Expressivity of Markov Reward
Dave Abel · Will Dabney · Anna Harutyunyan · Mark Ho · Michael Littman · Doina Precup · Satinder Singh

Tue Dec 07 01:20 AM -- 01:35 AM (PST) @ None

Reward is the driving force for reinforcement-learning agents. This paper is dedicated to understanding the expressivity of 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” that might be desirable: (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 optimize tasks of each of these three types, and correctly determine when no such reward function exists. We conclude with an empirical study that corroborates and illustrates our theoretical findings.

Author Information

Dave Abel (DeepMind)
Will Dabney (DeepMind)
Anna Harutyunyan (DeepMind)
Mark Ho (Princeton University)
Michael Littman (Brown University)
Doina Precup (DeepMind)
Satinder Singh (DeepMind)

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