Learning secrets interactively. Dynamic modeling in inductive inference

Abstract

Introduced is a new inductive inference paradigm, dynamic modeling. Within this learning paradigm, for example, function h learns function g iff, in the i-th iteration, h and g both produce output, h gets the sequence of all outputs from g in prior iterations as input, g gets all the outputs from h in prior iterations as input, and, from some iteration on, the sequence of hʼs outputs will be programs for the output sequence of g.Dynamic modeling provides an idealization of, for example, a social interaction in which h seeks to discover program models of gʼs behavior it sees in interacting with g, and h openly discloses to g its sequence of candidate program models to see what g says back. Sample results: every g can be so learned by some h; there are g that can only be learned by an h if g can also learn that h back; there are extremely secretive h which cannot be learned back by any g they learn, but which, nonetheless, succeed in learning infinitely many g; quadratic time learnability is strictly more powerful than linear time learnability.This latter result, as well as others, follows immediately from general correspondence theorems obtained from a unified approach to the paradigms within inductive inference.Many proofs, some sophisticated, employ machine self-reference, a.k.a., recursion theorems.