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 $\\epsilon$-optimal ranking of the $n$ items with probability at least $1 – \\delta$. When the feedback in each subset round is a single Plackett-Luce-sampled item, we show $(\\epsilon, \\delta)$-PAC algorithms with a sample complexity of $O\\left(\\frac{n}{\\epsilon^2} \\ln \\frac{n}{\\delta} \\right)$ rounds, which we establish as being order-optimal by exhibiting a matching sample complexity lower bound of $\\Omega\\left(\\frac{n}{\\epsilon^2} \\ln \\frac{n}{\\delta} \\right)$—this shows that there is essentially no improvement possible from the pairwise comparisons setting ($k = 2$). When, however, it is possible to elicit top-$m$ ($\\leq k$) ranking feedback according to the PL model from each adaptively chosen subset of size $k$, we show that an $(\\epsilon, \\delta)$-PAC ranking sample complexity of $O\\left(\\frac{n}{m \\epsilon^2} \\ln \\frac{n}{\\delta} \\right)$ is achievable with explicit algorithms, which represents an $m$-wise 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 $O(n^2)$ pairwise score estimates that has been used in prior work. We report results of numerical experiments that corroborate our findings.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"PMLR","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"3312","msr_page_range_end":"3321","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"International Conference on Artificial Intelligence and 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