Learning Fast Optimizers for Contextual Stochastic Integer Programs

The constraints in the problem are known as non-anticipativity constraiants, since the enforce that x has to be chosen independent of the value of ω (i.e., at the first stage, we do not know the precise realization of the second stage randomness). We obtain a relaxation of the above problem by dropping the non-anticipativity constraints and simply adding a Lagrangian term that tries to enforce the constraint:

[1]  Demis Hassabis,et al.  Mastering the game of Go without human knowledge , 2017, Nature.

[2]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[3]  Samy Bengio,et al.  Neural Combinatorial Optimization with Reinforcement Learning , 2016, ICLR.

[4]  David L. Woodruff,et al.  Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems , 2011, Comput. Manag. Sci..

[5]  Andrew W. Moore,et al.  Learning Evaluation Functions to Improve Optimization by Local Search , 2001, J. Mach. Learn. Res..

[6]  Le Song,et al.  2 Common Formulation for Greedy Algorithms on Graphs , 2018 .

[7]  Benjamin Müller,et al.  The SCIP Optimization Suite 5.0 , 2017, 2112.08872.

[8]  Jianhui Wang,et al.  Stochastic Optimization for Unit Commitment—A Review , 2015, IEEE Transactions on Power Systems.

[9]  Wei Zhang,et al.  A Reinforcement Learning Approach to job-shop Scheduling , 1995, IJCAI.

[10]  Lewis Ntaimo,et al.  The Million-Variable “March” for Stochastic Combinatorial Optimization , 2005, J. Glob. Optim..

[11]  Le Song,et al.  Learning to Branch in Mixed Integer Programming , 2016, AAAI.

[12]  Alex Graves,et al.  Asynchronous Methods for Deep Reinforcement Learning , 2016, ICML.

[13]  Andrea Lodi,et al.  On learning and branching: a survey , 2017 .

[14]  Gilbert Laporte,et al.  The Vehicle Routing Problem with Stochastic Travel Times , 1992, Transp. Sci..

[15]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[16]  Ronald J. Williams,et al.  Simple Statistical Gradient-Following Algorithms for Connectionist Reinforcement Learning , 2004, Machine Learning.

[17]  George L. Nemhauser,et al.  Learning to Run Heuristics in Tree Search , 2017, IJCAI.

[18]  Rüdiger Schultz,et al.  Dual decomposition in stochastic integer programming , 1999, Oper. Res. Lett..

[19]  Geoffrey E. Hinton,et al.  The EM algorithm for mixtures of factor analyzers , 1996 .

[20]  Hugo Larochelle,et al.  The Neural Autoregressive Distribution Estimator , 2011, AISTATS.