We investigate the problem of learning the transition dynamics of deterministic, discrete-state environments. We assume that an agent exploring such an environment is able to perform actions (from a finite set of actions) in the environment and to sense the state changes. The question investigated is whether the agent can learn the dynamics without visiting all states. Such a goal is unrealistic in general, hence we assume that the environment has structural properties an agent might exploit. In particular, we assume that the set of all action sequences forms an algebraic group. We introduce a learning model in different variants and study under which circumstances the corresponding "group-structured environments" can be learned efficiently by experimenting with group generators (actions). It turns out that for some classes of such environments the choice of actions given to the agent determines if efficient learning is possible. Negative results are presented, even without efficiency constraints, for rather general classes of groups, showing that even with group structure, learning an environment from partial information is far from trivial. However, positive results for special subclasses of Abelian groups turn out to be a good starting point for the design of efficient learning algorithms based on structured representations. © 2009 Elsevier Inc. All rights reserved.
Bartók, G., Szepesvári, C., & Zilles, S. (2010). Models of active learning in group-structured state spaces. Information and Computation, 208(4), 364–384. https://doi.org/10.1016/j.ic.2009.09.001