  Offline Reinforcement Learning methods seek to learn a policy from logged
transitions of an environment, without any interaction. In the presence of
function approximation, and under the assumption of limited coverage of the
state-action space of the environment, it is necessary to enforce the policy to
visit state-action pairs close to the support of logged transitions. In this
work, we propose an iterative procedure to learn a pseudometric (closely
related to bisimulation metrics) from logged transitions, and use it to define
this notion of closeness. We show its convergence and extend it to the function
approximation setting. We then use this pseudometric to define a new lookup
based bonus in an actor-critic algorithm: PLOFF. This bonus encourages the
actor to stay close, in terms of the defined pseudometric, to the support of
logged transitions. Finally, we evaluate the method on hand manipulation and
locomotion tasks.
