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Combinatorial bandits with relative feedback

Saha, A and Gopalan, A (2019) Combinatorial bandits with relative feedback. In: 33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019, 8-14 December 2019, Vancouver; Canada.

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Official URL: https://arxiv.org/pdf/1903.00543.pdf

Abstract

We consider combinatorial online learning with subset choices when only relative feedback information from subsets is available, instead of bandit or semi-bandit feedback which is absolute. Specifically, we study two regret minimisation problems over subsets of a finite ground set n, with subset-wise relative preference information feedback according to the Multinomial logit choice model. In the first setting, the learner can play subsets of size bounded by a maximum size and receives top-m rank-ordered feedback, while in the second setting the learner can play subsets of a fixed size k with a full subset ranking observed as feedback. For both settings, we devise instance-dependent and order-optimal regret algorithms with regret O(mn ln T ) and O(nk ln T ), respectively. We derive fundamental limits on the regret performance of online learning with subset-wise preferences, proving the tightness of our regret guarantees. Our results also show the value of eliciting more general top-m rank-ordered feedback over single winner feedback (m = 1). Our theoretical results are corroborated with empirical evaluations. © 2019 Neural information processing systems foundation. All rights reserved.

Item Type: Conference Paper
Publication: Advances in Neural Information Processing Systems
Publisher: Neural information processing systems foundation
Additional Information: The copyright of this article belongs to Neural information processing systems foundation
Keywords: E-learning, Bandit feedbacks; Empirical evaluations; Feed back information; Minimisation; Multinomial Logit; Online learning; Optimal regret; Preference information, Set theory
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Division of Electrical Sciences > Electrical Communication Engineering > Electrical Communication Engineering - Technical Reports
Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems
Date Deposited: 09 Oct 2020 05:51
Last Modified: 09 Oct 2020 05:51
URI: http://eprints.iisc.ac.in/id/eprint/66563

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