Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Saving the phenomena: requirements that inductive inference machines not contradict known data
Information and Computation
On the role of procrastination in machine learning
Information and Computation
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Inductive Inference, DFAs, and Computational Complexity
AII '89 Proceedings of the International Workshop on Analogical and Inductive Inference
Generalized notions of mind change complexity
Information and Computation
Robust learning: rich and poor
Journal of Computer and System Sciences
Feasible Iteration of Feasible Learning Functionals
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
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In computational function learning in the limit, an algorithmic learnertries to find a program for a computable function ggiven successively more values of g, each time outputting a conjectured program for g. A learner is called postdictively completeiff all available data is correctly postdicted by each conjecture.Akama and Zeugmann presented, for each choice of natural number 茂戮驴, a relaxation to postdictive completeness: each conjecture is required to postdict only all except the last 茂戮驴seendata points.This paper extends this notion of delayed postdictive completeness from constantdelays to dynamicallycomputed delays. On the one hand, the delays can be different for different data points. On the other hand, delays no longer need to be by a fixed finite number, but any type of computable countdown is allowed, including, for example, countdown in a system of ordinal notations and in other graphs disallowing computableinfinitely descending counts.We extend many of the theorems of Akama and Zeugmann and provide some feasible learnability results. Regarding fairnessin feasible learning, one needs to limit use of tricks that postpone output hypotheses until there is enough time to "think" about them. We see, for polytime learning, postdictive completeness (and delayed variants): 1. allows somebut notall postponement tricks, and2. there is a surprisingly tight boundary, for polytime learning, between what postponement is allowed and what is not. For example: 1. the set of polytime computable functions ispolytime postdictively completely learnable employing some postponement, but2. the set of exptime computable functions, while polytime learnable with a little more postponement, is notpolytime postdictively completely learnable! We have that, for wa notation for 茂戮驴, the set of exptime functions ispolytime learnable with w-delayedpostdictive completeness. Also provided are generalizations to further, small constructive limit ordinals.