  We consider a cooperative learning scenario where a collection of networked
agents with individually owned classifiers dynamically update their
predictions, for the same classification task, through communication or
observations of each other's predictions. Clearly if highly influential
vertices use erroneous classifiers, there will be a negative effect on the
accuracy of all the agents in the network. We ask the following question: how
can we optimally fix the prediction of a few classifiers so as maximize the
overall accuracy in the entire network. To this end we consider an aggregate
and an egalitarian objective function. We show a polynomial time algorithm for
optimizing the aggregate objective function, and show that optimizing the
egalitarian objective function is NP-hard. Furthermore, we develop
approximation algorithms for the egalitarian improvement. The performance of
all of our algorithms are guaranteed by mathematical analysis and backed by
experiments on synthetic and real data.
