Active Learning of Group-Structured Environments

The question investigated in this paper is to what extent an input representation influences the success of learning, in particular from the point of view of analyzing agents that can interact with their environment. We investigate learning environments that have a group structure. We introduce a learning model in different variants and study under which circumstances group structures can be learned efficiently from experimenting with group generators (actions). 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.