A Primal-Dual Online Algorithm for Online Matching Problem in Dynamic Environments

Authors

  • Yu-Hang Zhou Alibaba Group
  • Peng Hu Alibaba Group
  • Chen Liang Alibaba Group
  • Huan Xu Alibaba Group
  • Guangda Huzhang Alibaba Group
  • Yinfu Feng Alibaba Group
  • Qing Da Alibaba Group
  • Xinshang Wang Alibaba Group
  • An-Xiang Zeng Alibaba Group

Keywords:

Online Learning & Bandits

Abstract

Recently, the online matching problem has attracted much attention due to its wide application on real-world decision-making scenarios. In stationary environments, by adopting the stochastic user arrival model, existing methods are proposed to learn dual optimal prices and are shown to achieve a fast regret bound. However, the stochastic model is no longer a proper assumption when the environment is changing, leading to an optimistic method that may suffer poor performance. In this paper, we study the online matching problem in dynamic environments in which the dual optimal prices are allowed to vary over time. We bound the dynamic regret of online matching problem by the sum of two quantities, including a regret of online max-min problem and a dynamic regret of online convex optimization (OCO) problem. Then we propose a novel online approach named Primal-Dual Online Algorithm (PDOA) to minimize both quantities. In particular, PDOA adopts the primal-dual framework by optimizing dual prices with the online gradient descent (OGD) algorithm to eliminate the online max-min problem's regret. Moreover, it maintains a set of OGD experts and combines them via an expert-tracking algorithm, which gives a sublinear dynamic regret bound for the OCO problem. We show that PDOA achieves an O(K sqrt{T(1+P_T)}) dynamic regret where K is the number of resources, T is the number of iterations and P_T is the path-length of any potential dual price sequence that reflects the dynamic environment. Finally, experiments on real applications exhibit the superiority of our approach.

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Published

2021-05-18

How to Cite

Zhou, Y.-H., Hu, P., Liang, C., Xu, H., Huzhang, G., Feng, Y., Da, Q., Wang, X., & Zeng, A.-X. (2021). A Primal-Dual Online Algorithm for Online Matching Problem in Dynamic Environments. Proceedings of the AAAI Conference on Artificial Intelligence, 35(12), 11160-11167. Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/17331

Issue

Section

AAAI Technical Track on Machine Learning V