Bad-Policy Density: A Measure of Reinforcement Learning Hardness
This provides a theoretical measure to assess reinforcement learning difficulty, which could help researchers and practitioners understand and compare environments, though it is incremental as it builds on existing policy analysis without introducing new learning algorithms.
The paper tackles the problem of quantifying why reinforcement learning is easy in some environments but hard in others by proposing a measure called bad-policy density, which calculates the fraction of deterministic stationary policies below a value threshold, and proves it has desirable properties and is NP-hard to compute but approximable in polynomial time.
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.