  Transfer learning across different reinforcement learning (RL) tasks is
becoming an increasingly valuable area of research. We consider a goal-based
multi-task RL framework and mechanisms by which previously solved tasks can
reduce sample complexity and regret when the agent is faced with a new task.
Specifically, we introduce two metrics on the state space that encode notions
of traversibility of the state space for an agent. Using these metrics a
topological covering is constructed by way of a set of landmark states in a
fully self-supervised manner. We show that these landmark coverings confer
theoretical advantages for transfer learning within the goal-based multi-task
RL setting. Specifically, we demonstrate three mechanisms by which landmark
coverings can be used for successful transfer learning. First, we extend the
Landmark Options Via Reflection (LOVR) framework to this new topological
covering; second, we use the landmark-centric value functions themselves as
features and define a greedy zombie policy that achieves near oracle
performance on a sequence of zero-shot transfer tasks; finally, motivated by
the second transfer mechanism, we introduce a learned reward function that
provides a more dense reward signal for goal-based RL. Our novel topological
landmark covering confers beneficial theoretical results, bounding the Q values
at each state-action pair. In doing so, we introduce a mechanism that performs
action-pruning at infeasible actions which cannot possibly be part of an
optimal policy for the current goal.
