Asymptotic non-learnability of universal agents with computable horizon functions

Inside the Muchnik Degrees: Discontinuity, Learnability, and Constructivism

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded-lear...

Robust commitments and partial reputation

How should agents shape a finite “reputational" history to their advantage knowing that others will be learning from that history? We focus on one leader interacting with multiple followers and show that in most non-zero-sum games, the traditional Stackelberg mixed commitment is very fragile to observational uncertainty. We propose robust commitment rules that anticipate being learned and show ...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Learnability of periodic activation functions: General results

On-line learning in the presence of continuous periodic activation functions is studied analytically. The effect of the ambiguity ~an infinite number of inputs with different local fields can produce the same output! on the learnability is examined. A universal interplay between the general features of the activation function ~wave number, parity, etc.! and the critical learning rate is found. ...

Random reals à la Chaitin with or without prefix-freeness

We give a general theorem that provides examples of n-random reals à la Chaitin, for every n ≥ 1; these are halting probabilities of partial computable functions that are universal by adjunction for the class of all partial computable functions, The same result holds for the class functions of partial computable functions with prefix-free domain. Thus, the usual technical requirement of prefix-...