  Exploration is one of the most important tasks in Reinforcement Learning, but
it is not well-defined beyond finite problems in the Dynamic Programming
paradigm (see Subsection 2.4). We provide a reinterpretation of exploration
which can be applied to any online learning method. We come to this definition
by approaching exploration from a new direction. After finding that concepts of
exploration created to solve simple Markov decision processes with Dynamic
Programming are no longer broadly applicable, we reexamine exploration. Instead
of extending the ends of dynamic exploration procedures, we extend their means.
That is, rather than repeatedly sampling every state-action pair possible in a
process, we define the act of modifying an agent to itself be explorative. The
resulting definition of exploration can be applied in infinite problems and
non-dynamic learning methods, which the dynamic notion of exploration cannot
tolerate. To understand the way that modifications of an agent affect learning,
we describe a novel structure on the set of agents: a collection of distances
(see footnote 7) $d_{a} \in A$, which represent the perspectives of each agent
possible in the process. Using these distances, we define a topology and show
that many important structures in Reinforcement Learning are well behaved under
the topology induced by convergence in the agent space.
