A dynamic learning algorithm for online matching problems with concave returns

•We consider the online matching problem with concave returns. It is the core model for ad allocation.•We propose a dynamic learning algorithm that achieves near-optimal performance for this problem.•Our approach is primal-dual based. We overcome the difficulty that arises due to the nonlinearity.•W...

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Veröffentlicht in:European journal of operational research Jg. 247; H. 2; S. 379 - 388
Hauptverfasser: Chen, Xiao Alison, Wang, Zizhuo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.12.2015
Elsevier Sequoia S.A
Schlagworte:
Adwords problem
Algorithms
Allocations
Artificial intelligence
Decision analysis
Dynamic price update
Mathematical functions
Mathematical problems
Online algorithms
Optimization algorithms
Primal-dual
Random permutation model
Studies
Online algorithms
Adwords problem
Dynamic price update
Random permutation model
Primal-dual
ISSN:0377-2217, 1872-6860
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Zusammenfassung:•We consider the online matching problem with concave returns. It is the core model for ad allocation.•We propose a dynamic learning algorithm that achieves near-optimal performance for this problem.•Our approach is primal-dual based. We overcome the difficulty that arises due to the nonlinearity.•We test our algorithm using experimental data and show that it outperforms a myopic approach. We consider an online matching problem with concave returns. This problem is a generalization of the traditional online matching problem and has vast applications in online advertising. In this work, we propose a dynamic learning algorithm that achieves near-optimal performance for this problem when the inputs arrive in a random order and satisfy certain conditions. The key idea of our algorithm is to learn the input data pattern dynamically: we solve a sequence of carefully chosen partial allocation problems and use their optimal solutions to assist with the future decisions. Our analysis belongs to the primal-dual paradigm; however, the absence of linearity of the objective function and the dynamic feature of the algorithm makes our analysis quite unique. We also show through numerical experiments that our algorithm performs well for test data.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2015.06.029