Bootstrapping, uncertain semantics, and invariance

In the problem of bootstrapping, an agent learns to use an unknown body, in an unknown world, starting from zero information about the models involved. This is a fascinating problem, which so far has not been given a proper formalization. In this paper, we give a rigorous definition of what it means for an agent to be able to use "uninterpreted" observations and commands: there are some disturbances, represented by group actions, that modify what we call "semantic maps". The range of disturbances tolerated by an agent indirectly encode the assumptions needed by the agent. We argue that the behavior of agent which claims optimality (in any sense) must actually be invariant to such disturbances, and we discuss several design principles which allow to obtain this invariance for observations nuisances.