Learning and consistency

Abstract

In designing learning algorithms it seems quite reasonable to construct them in such a way that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail. It may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. Therefore we study several types of consistent learning in recursion-theoretic inductive inference. We show that these types are not of universal power. We give "lower bounds" on this power. We characterize these types by some versions of decidability of consistency with respect to suitable "non-standard" spaces of hypotheses. Then we investigate the problem of learning consistently in polynomial time. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to work inconsistently.

On some open problems in reflective inductive inference

“…As Fin ⊆ RCons ⊆ Cons (this holds also for each of the reflection models) [WZ95,Gri08], we have the following corollary.…”

“…For Ex and Fin criteria this does not make a difference, though it does make a difference for consistent learning (see for example, [BB75,WZ95,Gri08]). Moreover, for optimistic, pessimistic or exact reflection (for any of the criteria of learning considered in this paper), considering only canonical sequences does make a difference (see [Gri08]).…”

Inductive Inference and Language Learning

“…Though consistency seems to be a very natural requirement at first glance, it is not as many results show. We refer the interested reader to Wiehagen and Zeugmann [19] for a detailed discussion.…”

Consistency Conditions for Inductive Inference of Recursive Functions

“…The reader is encouraged to consult e.g., Jain et al [11], Fulk [7], Freivalds, Kinber and Wiehagen [6] and Wiehagen and Zeugmann [22,23] for further investigations concerning consistent and inconsistent learning.…”