A Near-Optimal Exploration-Exploitation Approach for Assortment Selection

Agrawal, Shipra; Avadhanula, Vashist; Goyal, Vineet; Zeevi, Assaf

doi:10.1145/2940716.2940779

Cited by 37 publications

(84 citation statements)

References 2 publications

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“…Finally, there is still a gap of O(log T ) between our Theorem 1 and the regret upper bounds established in [1]. We leave this as another interesting open question.…”

Section: Introductionmentioning

confidence: 81%

A note on a tight lower bound for capacitated MNL-bandit assortment selection models

Chen

2018

Operations Research Letters

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“…Finally, there is still a gap of O(log T ) between our Theorem 1 and the regret upper bounds established in [1]. We leave this as another interesting open question.…”

Section: Introductionmentioning

confidence: 81%

A note on a tight lower bound for capacitated MNL-bandit assortment selection models

Chen

2018

Operations Research Letters

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“…17 On a final note, one of our minor results -the improved confidence radius from Section 4.2may be of independent interest. In particular, this result is essential for some of the main results in (Babaioff et al, 2015a;Badanidiyuru et al, 2018;Agrawal and Devanur, 2014;Agrawal et al, 2016), in the context of dynamic pricing and other MAB problems with global supply/budget constraints.…”

Section: Follow-up Workmentioning

confidence: 96%

Bandits and Experts in Metric Spaces

Kleinberg

Slivkins

Upfal

2019

J. ACM

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In a multi-armed bandit problem, an online algorithm chooses from a set of strategies in a sequence of trials so as to maximize the total payoff of the chosen strategies. While the performance of bandit algorithms with a small finite strategy set is quite well understood, bandit problems with large strategy sets are still a topic of very active investigation, motivated by practical applications such as online auctions and web advertisement. The goal of such research is to identify broad and natural classes of strategy sets and payoff functions which enable the design of efficient solutions.In this work we study a very general setting for the multi-armed bandit problem in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric. We refer to this problem as the Lipschitz MAB problem. We present a solution for the multi-armed bandit problem in this setting. That is, for every metric space we define an isometry invariant which bounds from below the performance of Lipschitz MAB algorithms for this metric space, and we present an algorithm which comes arbitrarily close to meeting this bound. Furthermore, our technique gives even better results for benign payoff functions. We also address the full-feedback ("best expert") version of the problem, where after every round the payoffs from all arms are revealed. respectively). Compared to the conference publications, the manuscript contains full proofs and a significantly revised presentation. In particular, it develops new terminology and modifies the proof outlines to unify the technical exposition of the two papers. The manuscript also features an updated discussion of the follow-up work and open questions. All results on the zooming algorithm and the max-min-covering dimension are from Kleinberg et al. (2008c); all results on regret dichotomies and on Lipschitz experts are from Kleinberg and Slivkins (2010).

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“…Most of these papers offer provable bounds on the optimal expected revenue as opposed to performance guarantees on the optimality gap. Furthermore, we expect future work to focus increasingly on learning problems that deal with the exploration-exploitation trade off faced when we drop the assumption of known parameters of the demand model, such as the paper of Agrawal et al (2016).…”

Section: Discussionmentioning

confidence: 99%