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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 sampledaccording to a general Random Utility Model (RUM) with independent noiseperturbations to the latent item utilities. We identify a new property of sucha RUM, termed the minimum advantage, that helps in characterizing thecomplexity of separating pairs of items based on their relative win/lossempirical counts, and can be bounded as a function of the noise distributionalone. We give a learning algorithm for general RUMs, based on pairwiserelative counts of items and hierarchical elimination, along with a new PACsample complexity guarantee of $O(\frac{n}{c^2\epsilon^2} \log\frac{k}{\delta})$ rounds to identify an $\epsilon$-optimal item withconfidence $1-\delta$, when the worst case pairwise advantage in the RUM hassensitivity at least $c$ to the parameter gaps of items. Fundamental lowerbounds on PAC sample complexity show that this is near-optimal in terms of itsdependence on $n,k$ and $c$.

Best-item Learning in Random Utility Models with Subset Choices