Online Stochastic Optimization in the Large: Application to Kidney Exchange

Kidneys are the most prevalent organ transplants, but demand dwarfs supply. Kidney exchanges enable willing but incompatible donor-patient pairs to swap donors. These swaps can include cycles longer than two pairs as well, and chains triggered by altruistic donors. Current kidney exchanges address clearing (deciding who gets kidneys from whom) as an offline problem: they optimize the current batch. In reality, clearing is an online problem where patient-donor pairs and altruistic donors appear and expire over time. In this paper, we study trajectory-based online stochastic optimization algorithms (which use a recent scalable optimal offline solver as a subroutine) for this. We identify tradeoffs in these algorithms between different parameters. We also uncover the need to set the batch size that the algorithms consider an atomic unit. We develop an experimental methodology for setting these parameters, and conduct experiments on real and generated data. We adapt the REGRETS algorithm of Bent and van Hentenryck for the setting. We then develop a better algorithm. We also show that the AMSAA algorithm of Mercier and van Hentenryck does not scale to the nationwide level. Our best online algorithm saves significantly more lives than the current practice of solving each batch separately.

[1]  Yoav Freund,et al.  Experiments with a New Boosting Algorithm , 1996, ICML.

[2]  J. Ross Quinlan,et al.  C4.5: Programs for Machine Learning , 1992 .

[3]  Russell Bent,et al.  Waiting and Relocation Strategies in Online Stochastic Vehicle Routing , 2007, IJCAI.

[4]  Anders Krogh,et al.  Neural Network Ensembles, Cross Validation, and Active Learning , 1994, NIPS.

[5]  Padraig Cunningham,et al.  Diversity versus Quality in Classification Ensembles Based on Feature Selection , 2000, ECML.

[6]  Avrim Blum,et al.  Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges , 2007, EC '07.

[7]  Ian H. Witten,et al.  Data mining: practical machine learning tools and techniques with Java implementations , 2002, SGMD.

[8]  Ludmila I. Kuncheva,et al.  Measures of Diversity in Classifier Ensembles and Their Relationship with the Ensemble Accuracy , 2003, Machine Learning.

[9]  M. Utku Ünver,et al.  Dynamic Kidney Exchange , 2007 .

[10]  J. Davenport.  Editor , 1960 .

[11]  Xin Yao,et al.  Ensemble learning via negative correlation , 1999, Neural Networks.

[12]  Eric Bauer,et al.  An Empirical Comparison of Voting Classification Algorithms: Bagging, Boosting, and Variants , 1999, Machine Learning.

[13]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[14]  Zoubin Ghahramani,et al.  Proceedings of the 24th international conference on Machine learning , 2007, ICML 2007.

[15]  R. Ravi,et al.  What About Wednesday? Approximation Algorithms for Multistage Stochastic Optimization , 2005, APPROX-RANDOM.

[16]  Thomas G. Dietterich.  Multiple Classifier Systems , 2000, Lecture Notes in Computer Science.

[17]  K. Fernow.  New York , 1896, American Potato Journal.

[18]  David A. Cohn,et al.  Improving generalization with active learning , 1994, Machine Learning.

[19]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

[20]  Pascal Van Hentenryck,et al.  Amsaa: A Multistep Anticipatory Algorithm for Online Stochastic Combinatorial Optimization , 2008, CPAIOR.

[21]  Blai Bonet,et al.  Learning Depth-First Search: A Unified Approach to Heuristic Search in Deterministic and Non-Deterministic Settings, and Its Application to MDPs , 2006, ICAPS.

[22]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[23]  R. Ravi,et al.  Boosted sampling: approximation algorithms for stochastic optimization , 2004, STOC '04.

[24]  Sebastian Thrun,et al.  Text Classification from Labeled and Unlabeled Documents using EM , 2000, Machine Learning.

[25]  Stefanos A. Zenios,et al.  Optimal Control of a Paired-Kidney Exchange Program , 2002, Manag. Sci..

[26]  Pascal Van Hentenryck,et al.  Performance Analysis of Online Anticipatory Algorithms for Large Multistage Stochastic Integer Programs , 2007, IJCAI.

[27]  Pascal Van Hentenryck,et al.  AMSAA: an Anticipatory Algorithm for Online Stochastic Combinatorial Optimization , 2009 .

[28]  Russell Bent,et al.  Online stochastic reservation systems , 2009, Ann. Oper. Res..

[29]  D. Opitz,et al.  Popular Ensemble Methods: An Empirical Study , 1999, J. Artif. Intell. Res..

[30]  Russell Bent,et al.  Regrets Only! Online Stochastic Optimization under Time Constraints , 2004, AAAI.

[31]  Craig Boutilier,et al.  Expressive Banner Ad Auctions and Model-Based Online Optimization for Clearing , 2008, AAAI.

[32]  J. Ross Quinlan,et al.  Bagging, Boosting, and C4.5 , 1996, AAAI/IAAI, Vol. 1.

[33]  Russell Bent,et al.  Online Stochastic Reservation Systems , 2006, CPAIOR.

[34]  Geoffrey I. Webb,et al.  MultiBoosting: A Technique for Combining Boosting and Wagging , 2000, Machine Learning.

[35]  M. Utku Ünver,et al.  Increasing the Opportunity of Live Kidney Donation by Matching for Two- and Three-Way Exchanges , 2006, Transplantation.

[36]  Bruce E. Rosen,et al.  Ensemble Learning Using Decorrelated Neural Networks , 1996, Connect. Sci..

[37]  Thomas G. Dietterich.  What is machine learning? , 2020, Archives of Disease in Childhood.

[38]  Padraig Cunningham,et al.  Using Diversity in Preparing Ensembles of Classifiers Based on Different Feature Subsets to Minimize Generalization Error , 2001, ECML.

[39]  Oleksandr Makeyev,et al.  Neural network with ensembles , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[40]  David W. Opitz,et al.  Actively Searching for an E(cid:11)ective Neural-Network Ensemble , 1996 .