Best-item Learning in Random Utility Models with Subset Choices
This work addresses the challenge of efficient item selection in preference learning with noisy feedback, representing an incremental advance in algorithmic design for subset-based comparisons.
The paper tackles the problem of PAC learning the best item from a pool using subset choices under a Random Utility Model, achieving a near-optimal sample complexity of O(n/(c^2ε^2) log(k/δ)) rounds to identify an ε-optimal item with high confidence.
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 $O(\frac{n}{c^2ε^2} \log \frac{k}δ)$ rounds to identify an $ε$-optimal item with confidence $1-δ$, 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 $c$.