Active ranking with subset-wise preferences

Saha, A and Gopalan, A (2020) Active ranking with subset-wise preferences. In: 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019, 16 - 18 April 2019, LOISIR Hotel NahaNaha; Japan.

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Abstract

We consider the problem of probably approximately correct (PAC) ranking n items by adaptively eliciting subset-wise preference feedback. At each round, the learner chooses a subset of k items and observes stochastic feedback indicating preference information of the winner (most preferred) item of the chosen subset drawn according to a Plackett-Luce (PL) subset choice model unknown a priori. The objective is to identify an ε-optimal ranking of the n items with probability at least 1 − δ. When the feedback in each subset round is a single Plackett-Luce-sampled item, we show (ε, δ)-PAC algorithms with a sample complexity of O ( ε n2 ln nδ ) rounds, which we establish as being order-optimal by exhibiting a matching sample complexity lower bound of Ω ( ε n2 ln nδ )-this shows that there is essentially no improvement possible from the pairwise comparisons setting (k = 2). When, however, it is possible to elicit top-m (≤ k) ranking feedback according to the PL model from each adaptively chosen subset of size k, we show that an (ε, δ)-PAC ranking sample complexity of O ( mεn2 ln nδ ) is achievable with explicit algorithms, which represents an mwise reduction in sample complexity compared to the pairwise case. This again turns out to be order-wise unimprovable across the class of symmetric ranking algorithms. Our algorithms rely on a novel pivot trick to maintain only n itemwise score estimates, unlike O(n2) pairwise score estimates that has been used in prior work. We report results of numerical experiments that corroborate our findings.

Item Type:	Conference Paper
Publication:	AISTATS 2019 - 22nd International Conference on Artificial Intelligence and Statistics
Publisher:	PLMR
Additional Information:	The copyright of the article belongs to PLMR.
Keywords:	Artificial intelligence; Stochastic models; Stochastic systems, Explicit algorithms; Lower bounds; Numerical experiments; Pair-wise comparison; Preference information; Probably approximately correct; Ranking algorithm; Sample complexity, Set theory
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	13 Oct 2020 11:42
Last Modified:	08 Dec 2022 10:46
URI:	https://eprints.iisc.ac.in/id/eprint/65633

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