Peter I. Frazier
Assistant Professor
School of Operations Research
   and Information Engineering
Cornell University


Curriculum vitae

I am interested in a broad collection of problems. Most frequently I work on problems in simulation optimization and the global optimization of expensive functions, but I have also worked on problems in computer vision, logistics, information retrieval, neuroscience, inventory control, and drug discovery. Although they come from different disciplines, all of these problems are tied together by a common question: what is the most efficient way to collect information?

I study these questions within a mathematical framework that uses decision theory to pose the problem of collecting information in an optimal way as a Markov decision process (MDP). I then study the solutions of these MDPs using dynamic programming. This set of mathematical problems and tools is most frequently called sequential design of experiments, but it is also related to reinforcement learning, decision theory, active learning, budgeted learning, and multi-armed bandits. I often refer to it as optimal learning because we are asking how we can learn optimally.

My PhD thesis developed knowledge-gradient methods, a class of sequential Bayesian information collection methods that balance the cost and benefit of collecting information. I have also received AFOSR Young Investigator and NSF CAREER awards to study Bayesian methods in simulation optimization.

Introductory Materials


Journal Publications

  1. J. Xie & Frazier, Sequential Bayes-Optimal Policies for Multiple Comparisons with a Control, Operations Research, to appear. [PDF, Abstract]
  2. R. Waeber, Frazier & S.G. Henderson,, Bisection Search with Noisy Responses, SIAM Journal on Control and Optimization, 2013. [PDF, Abstract]
  3. S.C. Clark, R. Egan, Frazier, & Z. Wang,, ALE: a Generic Assembly Likelihood Evaluation Framework for Assessing the Accuracy of Genome and Metagenome Assemblies, Bioinformatics, 2013. [PDF, Abstract]
  4. L.H. Lee, E.P. Chew, Frazier, Q.S. Jia, & C.H. Chen, Advances in Simulation Optimization and its Applications, IIE Transactions, 2013. [Abstract]
  5. S.E. Chick & Frazier, Sequential Sampling with Economics of Selection Procedures, Management Science, 2012. [PDF, Abstract]
  6. I.O. Ryzhov, W.B. Powell & Frazier, The Knowledge-Gradient Algorithm for a General Class of Online Learning Problems, Operations Research, 2012. [PDF, Abstract]
  7. R. Waeber, Frazier & S.G. Henderson, A Framework for Selecting a Selection Procedure, ACM Transactions on Modeling and Computer Simulation, 2012. [PDF, Abstract]
  8. B. Jedynak, Frazier & R. Sznitman, Twenty Questions with Noise: Bayes Optimal Policies for Entropy Loss, Journal of Applied Probability, 2012. [PDF, Abstract]
  9. A.J. Meltzer, A. Graham, P.H. Connolly, J.K. Karwowski, H.L. Bush, Frazier & D.B. Schneider, Risk Factors for Early Failure after Peripheral Endovascular Intervention: Application of a Reliability Engineering Approach, Annals of Vascular Surgery, 2012. [PDF, Abstract]
  10. M.R.K. Mes, W.B. Powell & Frazier, Hierarchical Knowledge Gradient for Sequential Sampling, Journal of Machine Learning Research, 2011. [PDF, Abstract]
  11. W. Scott, Frazier & W.B. Powell, The Correlated Knowledge Gradient for Simulation Optimization of Continuous Parameters Using Gaussian Process Regression, SIAM Journal on Optimization, 2011. [PDF, Abstract]
  12. D. Negoescu, Frazier & W.B. Powell, The Knowledge-Gradient Algorithm for Sequencing Experiments in Drug Discovery, INFORMS Journal on Computing, 2011. [PDF, Abstract, Slides]
  13. D.M. Blei & Frazier, Distance Dependent Chinese Restaurant Processes, Journal of Machine Learning Research, 2011. [PDF, Abstract]
  14. Frazier & W.B. Powell, Consistency of Sequential Bayesian Sampling Policies, SIAM Journal on Control and Optimization, 2011. [PDF, Abstract, Slides]
  15. Frazier & W.B. Powell, Paradoxes in Learning and the Marginal Value of Information, Decision Analysis, 2010. [PDF, Abstract, Slides]
  16. Frazier, W.B. Powell & S. Dayanik, The Knowledge-Gradient Policy for Correlated Normal Beliefs, INFORMS Journal on Computing, 2009. [PDF, Abstract, Slides]
  17. Frazier, W.B. Powell & S. Dayanik, A Knowledge-Gradient Policy for Sequential Information Collection, SIAM Journal on Control and Optimization, 2008. [PDF, Abstract, Slides]

Working Papers

  1. Frazier, A Fully Sequential Elimination Procedure for Indifference-Zone Ranking and Selection with Tight Bounds on Probability of Correct Selection, in review . [PDF, Abstract, Slides]
  2. J. Xie, Frazier, & S.E. Chick, Bayesian Optimization via Simulation with Pairwise Sampling and Correlated Prior Beliefs, in review. [Abstract]
  3. S.J. Gershman, Frazier, D.M. Blei, Distance Dependent Infinite Latent Feature Models, in review. [PDF, Abstract]
  4. I.O. Ryzhov, Frazier & W.B. Powell, A New Optimal Stepsize Rule for Approximate Dynamic Programming, in review. [Abstract]
  5. D. Negoescu, Frazier & W.B. Powell, Optimal Learning Policies for the Newsvendor Problem with Censored Demand and Unobservable Lost Sales, in preparation. [PDF, Abstract]

Conference Publications

  1. J. Xie & Frazier,, Upper Bounds for Bayesian Ranking \amp; Selection, Winter Simulation Conference, 2013. [PDF, Abstract]
  2. R. Sznitman, A. Lucchi, B. Jedynak, Frazier, & P. Fua,, An Optimal Policy for Target Localization with Application to Electron Microscopy, International Conference on Machine Learning (ICML), 2013. [PDF, Abstract]
  3. Frazier, Tutorial: Optimization via Simulation with Bayesian Statistics and Dynamic Programming, Winter Simulation Conference, 2012. [PDF, Abstract, Slides]
  4. Frazier, B. Jedynak, & L. Chen, Sequential Screening: A Bayesian Dynamic Programming Analysis of Optimal Group-Splitting, Winter Simulation Conference, 2012. [PDF, Abstract, Slides]
  5. S. Zhang, P. Hanagal, Frazier, A.J. Meltzer, & D.B. Schneider, Optimal Patient-specific Postoperative Surveillance for Vascular Surgery, 7th INFORMS Workshop on Data Mining and Health Informatics 2012. [PDF, Abstract, Slides]
  6. J. Xie, Frazier, S. Sankaran, A. Marsden, & S. Elmohamed, Optimization of Computationally Expensive Simulations with Gaussian Processes and Parameter Uncertainty: Application to Cardiovascular Surgery, 50th Annual Allerton Conference on Communication, Control, and Computing, 2012. [PDF, Abstract, Slides]
  7. R. Waeber, Frazier & S.G. Henderson, A Bayesian Approach to Stochastic Root Finding, Winter Simulation Conference, 2011. [PDF, Abstract]
  8. Frazier, J. Xie & S.E. Chick, Bayesian Optimization via Simulation with Correlated Sampling and Correlated Prior Beliefs, Winter Simulation Conference, 2011. [PDF, Abstract, Slides]
  9. Frazier & A.M. Kazachkov, Guessing Preferences: A New Approach to Multi-Attribute Ranking and Selection, Winter Simulation Conference, 2011. [PDF, Abstract, Slides]
  10. R. Waeber, Frazier & S.G. Henderson, Performance Measures for Ranking and Selection Procedures, Winter Simulation Conference, 2010. [PDF, Abstract, Slides]
  11. D. Blei & Frazier , Distance Dependent Chinese Restaurant Processes, International Conference on Machine Learning, 2010. [PDF, Abstract]
  12. I.O. Ryzhov, Frazier & W.B. Powell, On the Robustness of a One-Period Look-Ahead Policy in Multi-Armed Bandit Problems, International Conference on Computational Stochastics, 2010. [PDF, Abstract]
  13. Frazier, W.B. Powell & H.P. Simao, Simulation Model Calibration with Correlated Knowledge-Gradients, Winter Simulation Conference, 2009. [PDF, Abstract, Slides]
  14. S. Chick & Frazier, The Conjunction of the Knowledge Gradient and the Economic Approach to Simulation Selection, Winter Simulation Conference, 2009. [PDF, Abstract, Slides]
  15. Frazier, W.B. Powell, S. Dayanik & P. Kantor, Approximate Dynamic Programming in Knowledge Discovery for Rapid Response, Hawaii International Conference on Systems Science, 2009. [PDF, Abstract]
  16. Frazier & W.B. Powell, The Knowledge-Gradient Stopping Rule for Ranking and Selection, Winter Simulation Conference, 2008. [PDF, Abstract, Slides]
  17. Frazier & A.J. Yu, Sequential Hypothesis Testing under Stochastic Deadlines, Neural Information Processing Systems, 2007. [PDF, Abstract, Slides]
  18. Frazier & W.B. Powell, The Knowledge Gradient Policy for Offline Learning with Independent Normal Rewards, IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning, 2007. [PDF, Abstract, Slides]

Book Chapters and PhD Thesis

  1. Frazier, Decision-Theoretic Foundations of Simulation Optimization, Wiley Encyclopedia of Operations Research & Management Science, 2010. [PDF, Abstract]
  2. Frazier, Learning with Dynamic Programming, Wiley Encyclopedia of Operations Research & Management Science, 2010. [PDF, Abstract]
  3. W.B.Powell & Frazier, Optimal Learning, TutORials in Operations Research, INFORMS, 2008. [PDF, Abstract, Slides]
  4. Frazier, Knowledge-Gradient Methods for Statistical Learning, PhD Thesis, Princeton University, 2009. [PDF, Abstract, Slides]

Teaching

PhD Students

Animations

The two movies above illustrate how the correlated knowledge gradient method may be used to find the maximum of a continuous function when the only way to learn about this function is through noisy measurements. The red lines shows the current estimate of the unknown function as well as the uncertainty in this estimate. The blue circles are measurement points, and the black line (right plot) and green squares (left plot) show the true value of the function. See "The Knowledge-Gradient Policy for Correlated Normal Beliefs" above for more details.

The two movies above illustrate the independent knowledge gradient method finding the best of several discrete alternatives, again through noisy measurement. The right plot illustrates the case for which the method was designed, in which the discrete alternatives have no relationship to each other, while the left plot illustrates what happens when you use the independent knowledge gradient to find the maximum of a continuous function at discretized location. To obtain faster convergence for such continuous problems, one can use the correlated knowledge gradient instead.

Presentations

Software

See the software page.

Funding

(webpage last updated Oct 7, 2013)