Timezone: »
We study convex stochastic optimization problems where a noisy objective function value is observed after a decision is made. There are many stochastic optimization problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation for the joint distribution of state-outcome pairs to create weights for previous observations. The weights effectively group similar states. Those similar to the current state are used to create a convex, deterministic approximation of the objective function. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We offer two weighting schemes, kernel based weights and Dirichlet process based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour ahead wind commitment problem. Our results show Dirichlet process weights can offer substantial benefits over kernel based weights and, more generally, that nonparametric estimation methods provide good solutions to otherwise intractable problems.
Author Information
Lauren A Hannah (Duke University)
Warren B Powell (Princeton University)
David Blei (Columbia University)
More from the Same Authors
-
2014 Workshop: Advances in Variational Inference »
David Blei · Shakir Mohamed · Michael Jordan · Charles Blundell · Tamara Broderick · Matthew D. Hoffman -
2014 Poster: A Filtering Approach to Stochastic Variational Inference »
Neil Houlsby · David Blei -
2014 Poster: Smoothed Gradients for Stochastic Variational Inference »
Stephan Mandt · David Blei -
2014 Poster: Content-based recommendations with Poisson factorization »
Prem Gopalan · Laurent Charlin · David Blei -
2013 Workshop: Topic Models: Computation, Application, and Evaluation »
David Mimno · Amr Ahmed · Jordan Boyd-Graber · Ankur Moitra · Hanna Wallach · Alexander Smola · David Blei · Anima Anandkumar -
2013 Workshop: Probabilistic Models for Big Data »
Neil D Lawrence · Joaquin QuiƱonero-Candela · Tianshi Gao · James Hensman · Zoubin Ghahramani · Max Welling · David Blei · Ralf Herbrich -
2013 Poster: Efficient Online Inference for Bayesian Nonparametric Relational Models »
Dae Il Kim · Prem Gopalan · David Blei · Erik Sudderth -
2013 Poster: Modeling Overlapping Communities with Node Popularities »
Prem Gopalan · Chong Wang · David Blei -
2012 Poster: Truncation-free Online Variational Inference for Bayesian Nonparametric Models »
Chong Wang · David Blei -
2012 Poster: Scalable Inference of Overlapping Communities »
Prem Gopalan · David Mimno · Sean Gerrish · Michael Freedman · David Blei -
2012 Spotlight: Scalable Inference of Overlapping Communities »
Prem Gopalan · David Mimno · Sean Gerrish · Michael Freedman · David Blei -
2012 Poster: How They Vote: Issue-Adjusted Models of Legislative Behavior »
Sean Gerrish · David Blei -
2011 Poster: Spatial distance dependent Chinese Restaurant Process for image segmentation »
Soumya Ghosh · Andrei B Ungureanu · Erik Sudderth · David Blei -
2010 Session: Oral Session 18 »
David Blei -
2010 Spotlight: Online Learning for Latent Dirichlet Allocation »
Matthew D. Hoffman · David Blei · Francis Bach -
2010 Poster: Online Learning for Latent Dirichlet Allocation »
Matthew D. Hoffman · David Blei · Francis Bach -
2009 Workshop: Applications for Topic Models: Text and Beyond »
David Blei · Jordan Boyd-Graber · Jonathan Chang · Katherine Heller · Hanna Wallach -
2009 Poster: Reading Tea Leaves: How Humans Interpret Topic Models »
Jonathan Chang · Jordan Boyd-Graber · Sean Gerrish · Chong Wang · David Blei -
2009 Oral: Reading Tea Leaves: How Humans Interpret Topic Models »
Jonathan Chang · Jordan Boyd-Graber · Sean Gerrish · Chong Wang · David Blei -
2009 Poster: Decoupling Sparsity and Smoothness in the Discrete Hierarchical Dirichlet Process »
Chong Wang · David Blei -
2009 Spotlight: Decoupling Sparsity and Smoothness in the Discrete Hierarchical Dirichlet Process »
Chong Wang · David Blei -
2009 Poster: Variational Inference for the Nested Chinese Restaurant Process »
Chong Wang · David Blei -
2009 Poster: A Bayesian Analysis of Dynamics in Free Recall »
Richard Socher · Samuel J Gershman · Adler Perotte · Per Sederberg · David Blei · Kenneth Norman -
2008 Workshop: Analyzing Graphs: Theory and Applications »
Edo M Airoldi · David Blei · Jake M Hofman · Tony Jebara · Eric Xing -
2008 Poster: Mixed Membership Stochastic Blockmodels »
Edo M Airoldi · David Blei · Stephen E Fienberg · Eric Xing -
2008 Spotlight: Mixed Membership Stochastic Blockmodels »
Edo M Airoldi · David Blei · Stephen E Fienberg · Eric Xing -
2008 Poster: Syntactic Topic Models »
Jordan Boyd-Graber · David Blei -
2008 Poster: Relative Performance Guarantees for Approximate Inference in Latent Dirichlet Allocation »
Indraneel Mukherjee · David Blei -
2008 Spotlight: Syntactic Topic Models »
Jordan Boyd-Graber · David Blei -
2008 Spotlight: Relative Performance Guarantees for Approximate Inference in Latent Dirichlet Allocation »
Indraneel Mukherjee · David Blei -
2007 Poster: Supervised Topic Models »
David Blei · Jon McAuliffe