Regular grammars are not learnable, but deterministic finite automata are learnable under various paradigms (Angluin, 1987).
it is possible to learn by changing to representations that have better properties: in particular DFAs are learnable because they are "objective"; there is a correspondence between the structure of the language, (the residual languages) and the representational primitives of the formalism (the states) which is expressed by the Myhill-Nerode theorem.