We study the construction of prediction algorithms in a situation in which a learner faces a sequence of trials with a prediction to be made in each and the goal of the learner is to make few mistakes We are interested in the case that the learner has reason to believe that one of some pool of known algorithms will perform well but the learner does not know which one A simple and e ective metho...

we only show one further result that emphasizes our point that understanding LMP is fundamental to understanding any generalization of this process. A simple generalization of the local majority process would allow vertex v to have some resistivity towards color switch. Formally, for a nonnegative integer kv, we de ne a kv-local majority rule for vertex v: ct+1 v = ( ctv if jfw 2 Nv : ctw = ctv...

Suppose we are given a set of n balls {b1, . . . , bn} each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls {bi1 , bi2 , bi3}. As an answer to such a query we obtain (the index of) a majority ball, that is, a ball whose color is the same as the color of another ball from the triple. Our goal is to find a non-m...

We initiate a systematic study of linear sketching over F2. For a given Boolean function f : {0, 1}n → {0, 1} a randomized F2-sketch is a distributionM over d×nmatrices with elements over F2 such that Mx suffices for computing f(x) with high probability. We study a connection between F2-sketching and a two-player one-way communication game for the corresponding XOR-function. Our results show th...