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.
Bibliographical noteFunding Information:
We thank the anonymous referees for their insightful comments. The research of both authors is supported by National Science Foundation under research grant CMMI-1434541 .
© 2015 Elsevier B.V. and Association of European Operational Research Societies(EURO)with in the International Federation of Operational Research Societies(IFORS).All rights reserved.
- Adwords problem
- Dynamic price update
- Online algorithms
- Random permutation model