Another Look at Universal Individual Learning

In recent papers we have proposed an individual setting for the batch learning problem and showed that it is solved by a known variant of the Normalized Maximum Likelihood (NML) which we termed pNML. In this paper we present a different possible definition for the batch learning problem in the individual setting and show that it is solved by another known variant of the normalized maximum likelihood, which we denote by pNML2. We further derive an exact expression of the pNML2 for the linear regression problem. We use this result, along with known results and new upper and lower bounds over the regret of the pNML2 learner, to compare between the two learners.