  Although exploration in reinforcement learning is well understood from a
theoretical point of view, provably correct methods remain impractical. In this
paper we study the interplay between exploration and approximation, what we
call approximate exploration. Our main goal is to further our theoretical
understanding of pseudo-count based exploration bonuses (Bellemare et al.,
2016), a practical exploration scheme based on density modelling. As a warm-up,
we quantify the performance of an exploration algorithm, MBIE-EB (Strehl and
Littman, 2008), when explicitly combined with state aggregation. This allows us
to confirm that, as might be expected, approximation allows the agent to trade
off between learning speed and quality of the learned policy. Next, we show how
a given density model can be related to an abstraction and that the
corresponding pseudo-count bonus can act as a substitute in MBIE-EB combined
with this abstraction, but may lead to either under- or over-exploration. Then,
we show that a given density model also defines an implicit abstraction, and
find a surprising mismatch between pseudo-counts derived either implicitly or
explicitly. Finally we derive a new pseudo-count bonus alleviating this issue.

Machine Learning;Artificial Intelligence;Machine Learning