Best-item Learning in Random Utility Models with Subset Choices

Saha, A and Gopalan, A (2020) Best-item Learning in Random Utility Models with Subset Choices. In: 23rd International Conference on Artificial Intelligence and Statistics, AISTATS 2020, 26 - 28 August 2020, pp. 4281-4291.

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Abstract

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 (Equation presented) rounds to identify an ∊-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.

Item Type:	Conference Paper
Publication:	Proceedings of Machine Learning Research
Publisher:	ML Research Press
Additional Information:	The copyright for this article belongs to ML Research Press.
Keywords:	Independent noise; Item-based; Low bound; Near-optimal; Noise distribution; Noise perturbation; PAC learning; Property; Random utility model; Sample complexity, Learning algorithms
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	17 Jul 2023 10:17
Last Modified:	17 Jul 2023 10:17
URI:	https://eprints.iisc.ac.in/id/eprint/82440

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