  Exploration is a major challenge in reinforcement learning, especially for
high-dimensional domains that require function approximation. We propose
exploration objectives -- policy optimization objectives that enable downstream
maximization of any reward function -- as a conceptual framework to systematize
the study of exploration. Within this framework, we introduce a new objective,
$L_1$-Coverage, which generalizes previous exploration schemes and supports
three fundamental desiderata:
  1. Intrinsic complexity control. $L_1$-Coverage is associated with a
structural parameter, $L_1$-Coverability, which reflects the intrinsic
statistical difficulty of the underlying MDP, subsuming Block and Low-Rank
MDPs.
  2. Efficient planning. For a known MDP, optimizing $L_1$-Coverage efficiently
reduces to standard policy optimization, allowing flexible integration with
off-the-shelf methods such as policy gradient and Q-learning approaches.
  3. Efficient exploration. $L_1$-Coverage enables the first computationally
efficient model-based and model-free algorithms for online (reward-free or
reward-driven) reinforcement learning in MDPs with low coverability.
  Empirically, we find that $L_1$-Coverage effectively drives off-the-shelf
policy optimization algorithms to explore the state space.
