  We consider the problem of PAC learning the most valuable item from a pool of
$n$ items using sequential, adaptively chosen plays of subsets of $k$ items,
when, upon playing a subset, the learner receives relative feedback sampled
according to a general Random Utility Model (RUM) with independent noise
perturbations to the latent item utilities. We identify a new property of such
a RUM, termed the minimum advantage, that helps in characterizing the
complexity of separating pairs of items based on their relative win/loss
empirical counts, and can be bounded as a function of the noise distribution
alone. We give a learning algorithm for general RUMs, based on pairwise
relative counts of items and hierarchical elimination, along with a new PAC
sample complexity guarantee of $O(\frac{n}{c^2\epsilon^2} \log
\frac{k}{\delta})$ rounds to identify an $\epsilon$-optimal item with
confidence $1-\delta$, when the worst case pairwise advantage in the RUM has
sensitivity at least $c$ to the parameter gaps of items. Fundamental lower
bounds on PAC sample complexity show that this is near-optimal in terms of its
dependence on $n,k$ and $c$.
