  Reinforcement learning is hard in general. Yet, in many specific
environments, learning is easy. What makes learning easy in one environment,
but difficult in another? We address this question by proposing a simple
measure of reinforcement-learning hardness called the bad-policy density. This
quantity measures the fraction of the deterministic stationary policy space
that is below a desired threshold in value. We prove that this simple quantity
has many properties one would expect of a measure of learning hardness.
Further, we prove it is NP-hard to compute the measure in general, but there
are paths to polynomial-time approximation. We conclude by summarizing
potential directions and uses for this measure.
