  Classical learning assumes the learner is given a labeled data sample, from
which it learns a model. The field of Active Learning deals with the situation
where the learner begins not with a training sample, but instead with resources
that it can use to obtain information to help identify the optimal model. To
better understand this task, this paper presents and analyses the simplified
"(budgeted) active model selection" version, which captures the pure
exploration aspect of many active learning problems in a clean and simple
problem formulation. Here the learner can use a fixed budget of "model probes"
(where each probe evaluates the specified model on a random indistinguishable
instance) to identify which of a given set of possible models has the highest
expected accuracy. Our goal is a policy that sequentially determines which
model to probe next, based on the information observed so far. We present a
formal description of this task, and show that it is NPhard in general. We then
investigate a number of algorithms for this task, including several existing
ones (eg, "Round-Robin", "Interval Estimation", "Gittins") as well as some
novel ones (e.g., "Biased-Robin"), describing first their approximation
properties and then their empirical performance on various problem instances.
We observe empirically that the simple biased-robin algorithm significantly
outperforms the other algorithms in the case of identical costs and priors.
