  Coverage conditions -- which assert that the data logging distribution
adequately covers the state space -- play a fundamental role in determining the
sample complexity of offline reinforcement learning. While such conditions
might seem irrelevant to online reinforcement learning at first glance, we
establish a new connection by showing -- somewhat surprisingly -- that the mere
existence of a data distribution with good coverage can enable sample-efficient
online RL. Concretely, we show that coverability -- that is, existence of a
data distribution that satisfies a ubiquitous coverage condition called
concentrability -- can be viewed as a structural property of the underlying
MDP, and can be exploited by standard algorithms for sample-efficient
exploration, even when the agent does not know said distribution. We complement
this result by proving that several weaker notions of coverage, despite being
sufficient for offline RL, are insufficient for online RL. We also show that
existing complexity measures for online RL, including Bellman rank and
Bellman-Eluder dimension, fail to optimally capture coverability, and propose a
new complexity measure, the sequential extrapolation coefficient, to provide a
unification.
