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光华讲坛—Distributionally Robust Stochastic and Online Optimization

发布时间:2019-07-03

主讲人:美国斯坦福大学 叶荫宇教授
主持人:
工商管理学院院长 陈滨桐教授
时间:
2019年7月15日(星期一)10:00-12:00
地点:
西南财经大学柳林校区弘远楼109
主办单位:
工商管理学院、科研处

主讲人简介:
Yinyu Ye is currently the K.T. Li Chair Professor of Engineering at Department of Management Science and Engineering and Institute of Computational and Mathematical Engineering, Stanford University. He is also the Director of the MS&E Industrial Affiliates Program. He received the B.S. degree in System Engineering from the Huazhong University of Science and Technology, China, and the M.S. and Ph.D. degrees in Engineering-Economic Systems and Operations Research from Stanford University. His current research interests include Continuous and Discrete Optimization, Data Science and Application, Algorithm Design and Analysis, Computational Game/Market Equilibrium, Metric Distance Geometry, Dynamic Resource Allocation, and Stochastic and Robust Decision Making, etc. He is an INFORMS (The Institute for Operations Research and The Management Science) Fellow since 2012, and has received several academic awards including: the 2009 John von Neumann Theory Prize for fundamental sustained contributions to theory in Operations Research and the Management Sciences, the 2015 SPS Signal Processing Magazine Best Paper Award, the winner of the 2014 SIAM Optimization Prize awarded (every three years), the inaugural 2012 ISMP Tseng Lectureship Prize for outstanding contribution to continuous optimization (every three years), the inaugural 2006 Farkas Prize on Optimization, the 2009 IBM Faculty Award, etc.. He has supervised numerous doctoral students at Stanford who received the 2015 and 2013 Second Prize of INFORMS Nicholson Student Paper Competition, the 2013 INFORMS Computing Society Prize, the 2008 First Nicholson Prize, and the 2006 and 2010 INFORMS Optimization Prizes for Young Researchers. He is the Chairman of technical advisory board of MOSEK, one of the major commercial international optimization software companies. His text book written with David Luenberger, “Linear and Nonlinear Programming,” has been popularly used in academic education. In the past, Ye has led and managed a group of researchers on a broader range of government and industrial projects including Boeing, American Express, Oracle, AOL, IBM, 49ers, Huawei, EPRI, China EPRI, Ai-Force, NSF, DOE, etc.; focusing on business analytics, sensor network, big data, risk management, electronic commerce, Internet economics, etc. He has been the Director of the Stanford Management Science and Engineering Department Industrial Affiliates Program since 2002, where his role is to establish direct links between members of the faculty and industrial affiliates.
叶荫宇是斯坦福大学李国鼎工程首席教授(K. T. Li Chair Professor),现任美国斯坦福大学管理科学与工程系及计算数学工程研究院的杰出终身教授,也是斯坦福管理科学与工程系工业联盟主任。本科毕业于华中科技大学自动控制系 ,后赴美获斯坦福大学博士学位。他主要从事数学规划、优化算法设计与分析、计算复杂性、运筹学、物流及供应链方法、无线传感器网络、市场平衡及博弈论等研究。他也是优化领域基石算法之一——内点算法的奠基人之一。因贡献突出,他曾获得美国运筹与管理学会冯·诺依曼理论奖,也是迄今为止唯一获得此奖的华人学者。在业界,叶荫宇担任了优化软件公司 MOSEK 科技顾问委员会主席、杉数科技的首席科学顾问。


主要内容:

We present decision/optimization models/problems driven by uncertain and online data, and show how analytical models and computational algorithms can be used to achieve solution efficiency and near optimality.
First, we describe the so-called Distributionally or Likelihood Robust optimization (DRO) models and their algorithms in dealing stochastic decision problems when the exact uncertainty distribution is unknown but certain statistical moments and/or sample distributions can be estimated.
Secondly, when decisions are made in presence of high dimensional stochastic data, handling joint distribution of correlated random variables can present a formidable task, both in terms of sampling and estimation as well as algorithmic complexity. A common heuristic is to estimate only marginal distributions and substitute joint distribution by independent (product) distribution. Here, we study possible loss incurred on ignoring correlations through the DRO approach, and quantify that loss as Price of Correlations (POC).
Thirdly, we describe an online combinatorial auction problem using online linear programming technologies. We discuss near-optimal algorithms for solving this surprisingly general class of online problems under the assumption of random order of arrivals.
在现实生活中,我们通常会遇到一些在线的并带有不确定性的数据,以及由这些数据所生成的问题。今天我们讲的就是如何使用一些分析模型和算法来高效的找到这些问题的近似最优解。
首先,假设数据真实的分布是未知的,但我们知道数据的统计矩或者样本的分布可以被估计。那么我们可以使用基于分布的鲁棒优化模型(DRO)和算法来解决对应的随机决策问题。其次,当数据是高维且随机时,处理相关变量之间的联合分布无论是从采样估计还是算法复杂度方面都会变得非常困难。此时,一种常用的启发式算法是仅仅估计变量的边缘分布并使用独立分布来代替联合分布。对此情况,我们研究了这种启发式算法由于忽略相关性而带来的近似损失量会有多大,并由相关代价(POC)来定量表示。最后我们使用了在线线性规划技术来搭建了一个在线组合拍卖问题。在订单到达随机性的假设下,我们讨论了近似最优算法如何来解决这一大类的在线问题。



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