A Dynamic Near-Optimal Algorithm for Online Linear Programming
成果类型：
Article
署名作者：
Agrawal, Shipra; Wang, Zizhuo; Ye, Yinyu
署名单位：
Microsoft; Microsoft India; University of Minnesota System; University of Minnesota Twin Cities; Stanford University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.2014.1289
发表日期：
2014
页码：
876-890
关键词：
摘要：
A natural optimization model that formulates many online resource allocation problems is the online linear programming ( LP) problem in which the constraint matrix is revealed column by column along with the corresponding objective coefficient. In such a model, a decision variable has to be set each time a column is revealed without observing the future inputs, and the goal is to maximize the overall objective function. In this paper, we propose a near-optimal algorithm for this general class of online problems under the assumptions of random order of arrival and some mild conditions on the size of the LP right-hand-side input. Specifically, our learning-based algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from the revealed columns in the previous period are used to determine the sequential decisions in the current period. Through dynamic learning, the competitiveness of our algorithm improves over the past study of the same problem. We also present a worst case example showing that the performance of our algorithm is near optimal.
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