Semantic Communication for Simple Goals Is Equivalent to On-line Learning

Abstract

Previous works [11,6] introduced a model of semantic communication between a “user” and a “server,” in which the user attempts to achieve a given goal for communication. They show that whenever the user can sense progress, there exist universal user strategies that can achieve the goal whenever it is possible for any other user to reliably do so. A drawback of the actual constructions is that the users are inefficient: they enumerate protocols until they discover one that is successful, leading to the potential for exponential overhead in the length of the desired protocol. Goldreich et al. [6] conjectured that this overhead could be reduced to a polynomial dependence if we restricted our attention to classes of sufficiently simple user strategies and goals. In this work, we are able to obtain such universal strategies for some reasonably general special cases by establishing an equivalence between these special cases and the usual model of mistake-bounded on-line learning [3,15]. This equivalence also allows us to see the limits of constructing universal users based on sensing and motivates the study of sensing with richer kinds of feedback. Along the way, we also establish a new lower bound for the “beliefs model” [12], which demonstrates that constructions of efficient users in that framework rely on the existence of a common “belief” under which all of the servers in a class are designed to be efficient.

This work is also presented in Chapters 4 and 8 of the first author’s thesis [10].