A problem posed by Freund is how to efficiently track a small pool of experts
out of a much larger set. This problem was solved when Bousquet and Warmuth
introduced their mixing past posteriors (MPP) algorithm in 2001.

In Freund's problem the experts would normally be considered black boxes.
However, in this paper we re-examine Freund's problem in case the experts have
internal structure that enables them to learn. In this case the problem has two
possible interpretations: should the experts learn from all data or only from
the subsequence on which they are being tracked? The MPP algorithm solves the
first case. Our contribution is to generalise MPP to address the second option.
The results we obtain apply to any expert structure that can be formalised
using (expert) hidden Markov models. Curiously enough, for our interpretation
there are \emph{two} natural reference schemes: freezing and sleeping. For each
scheme, we provide an efficient prediction strategy and prove the relevant loss
bound.