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From pac to instance-optimal sample complexity in the plackett-luce model

Saha, A and Gopalan, A (2020) From pac to instance-optimal sample complexity in the plackett-luce model. In: 37th International Conference on Machine Learning, ICML 2020, 13-18 July 2020, pp. 8336-8345.

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We consider PAC-learning a good item from k- subsetwise feedback information sampled from a Plackett-Luce probability model, with instancedependent sample complexity performance. In the setting where subsets of a fixed size can be tested and top-ranked feedback is made available to the learner, we give an algorithm with optimal instance-dependent sample complexity, for PAC best arm identification, of (�k/k Σni=2 max (1, 1/�2i) ln k/δ ( ln 1/�i)), �i being the Plackett-Luce parameter gap between the best and the ith best item, and �k is the sum of the Plackett-Luce parameters for the top-k items. The algorithm is based on a wrapper around a PAC winner-finding algorithm with weaker performance guarantees to adapt to the hardness of the input instance. The sample complexity is also shown to be multiplicatively better depending on the length of rank-ordered feedback available in each subset-wise play. We show optimality of our algorithms with matching sample complexity lower bounds. We next address the winner-finding problem in Plackett-Luce models in the fixed-budget setting with instance dependent upper and lower bounds on the misidentification probability, of Ω (exp(-2�Q)) for a given budget Q, where � is an explicit instancedependent problem complexity parameter. Numerical performance results are also reported. Copyright © 2020 by the Authors. All rights reserved.

Item Type: Conference Paper
Publication: 37th International Conference on Machine Learning, ICML 2020
Publisher: International Machine Learning Society (IMLS)
Additional Information: The copyright for this article belongs to International Machine Learning Society (IMLS)
Keywords: Machine learning, Feed back information; Misidentification probability; Numerical performance; Performance guarantees; Probability modeling; Problem complexity; Sample complexity; Upper and lower bounds, Budget control
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 04 Aug 2021 06:19
Last Modified: 04 Aug 2021 06:19
URI: http://eprints.iisc.ac.in/id/eprint/68986

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