Online Learning with Diverse User Preferences

Chao Gan, Jing Yang, Ruida Zhou, Cong Shen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we investigate the impact of diverse user preference on learning under the stochastic multi-armed bandit (MAB) framework. We aim to show that when the user preferences are sufficiently diverse and each arm is optimal for certain users, the O(log T ) regret incurred by exploring the sub-optimal arms under the standard stochastic MAB setting can be reduced to a constant. Our intuition is that to achieve sub-linear regret, the number of times an optimal arm being pulled should scale linearly in time; when all arms are optimal for certain users and pulled frequently, the estimated arm statistics can quickly converge to their true values, thus reducing the need of exploration dramatically. We cast the problem into a stochastic linear bandits model, where both user preferences and arm states are modeled as independent and identical distributed (i.i.d) d-dimensional random vectors. After receiving a user preference vector at the beginning of each time slot, the learner pulls an arm and receives a reward as the linear product of the preference vector and the arm state vector. We also assume that the state of the pulled arm is revealed to the learner once it is pulled. We propose a Weighted Upper Confidence Bound (W-UCB) algorithm and show that it can achieve a constant regret when the user preferences are sufficiently diverse. The performance of W-UCB under general setups is also completely characterized and validated with synthetic data.

Original languageEnglish (US)
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2539-2543
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: Jul 7 2019Jul 12 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period7/7/197/12/19

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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