  In this work, we propose an information-directed objective for
infinite-horizon reinforcement learning (RL), called the occupancy information
ratio (OIR), inspired by the information ratio objectives used in previous
information-directed sampling schemes for multi-armed bandits and Markov
decision processes as well as recent advances in general utility RL. The OIR,
comprised of a ratio between the average cost of a policy and the entropy of
its induced state occupancy measure, enjoys rich underlying structure and
presents an objective to which scalable, model-free policy search methods
naturally apply. Specifically, we show by leveraging connections between
quasiconcave optimization and the linear programming theory for Markov decision
processes that the OIR problem can be transformed and solved via concave
programming methods when the underlying model is known. Since model knowledge
is typically lacking in practice, we lay the foundations for model-free OIR
policy search methods by establishing a corresponding policy gradient theorem.
Building on this result, we subsequently derive REINFORCE- and
actor-critic-style algorithms for solving the OIR problem in policy parameter
space. Crucially, exploiting the powerful hidden quasiconcavity property
implied by the concave programming transformation of the OIR problem, we
establish finite-time convergence of the REINFORCE-style scheme to global
optimality and asymptotic convergence of the actor-critic-style scheme to
(near) global optimality under suitable conditions. Finally, we experimentally
illustrate the utility of OIR-based methods over vanilla methods in
sparse-reward settings, supporting the OIR as an alternative to existing RL
objectives.
