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Approximate Bayesian inference for simulation and optimization

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 147))

Abstract

We present an overview of approximate Bayesian methods for sequential learning in problems where conjugate Bayesian priors are unsuitable or unavailable. Such problems have numerous applications in simulation optimization, revenue management, e-commerce, and the design of competitive events. We discuss two important computational strategies for learning in such applications, and illustrate each strategy with multiple examples from the recent literature. We also briefly describe conjugate Bayesian models for comparison, and remark on the theoretical challenges of approximate models.

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References

  1. Blei, D.M., Jordan, M.I., Paisley, J.W.: Variational Bayesian inference with stochastic search. In: Proceedings of the 29th International Conference on Machine Learning, pp. 1367–1374 (2012)

    Google Scholar 

  2. Brahma, A., Chakraborty, M., Das, S., Lavoie, A., Magdon-Ismail, M.: A Bayesian market maker. In: Proceedings of the 13th ACM Conference on Electronic Commerce, pp. 215–232 (2012)

    Google Scholar 

  3. Chakraborty, M., Das, S., Lavoie, A., Magdon-Ismail, M., Naamad, Y.: Instructor rating markets. In: Proceedings of the 27th AAAI Conference on Artificial Intelligence, pp. 159–165 (2013)

    Google Scholar 

  4. Chau, M., Fu, M.C., Qu, H., Ryzhov, I.O.: Simulation optimization: a tutorial overview and recent developments in gradient-based methods. In: Tolk, A., Diallo, S.Y., Ryzhov, I.O., Yilmaz, L., Buckley, S., Miller, J.A. (eds.) Proceedings of the 2014 Winter Simulation Conference, pp. 21–35 (2014)

    Google Scholar 

  5. Chhabra, M., Das, S.: Learning the demand curve in posted-price digital goods auctions. In: Proceedings of the 10th International Conference on Autonomous Agents and Multi-Agent Systems, pp. 63–70 (2011)

    Google Scholar 

  6. Chien, Y.T., Fu, K.-S.: On Bayesian learning and stochastic approximation. IEEE Trans. Syst. Sci. Cybern. 3(1), 28–38 (1967)

    Article  Google Scholar 

  7. Cinlar, E.: Probability and Stochastics. Springer, New York (2011)

    Book  MATH  Google Scholar 

  8. Dangauthier, P., Herbrich, R., Minka, T.P., Graepel, T.: TrueSkill through time: revisiting the history of chess. In: Platt, J.C., Koller, D., Singer, Y., Roweis, S. (eds.) Advances in Neural Information Processing Systems, Curran Associates, Inc., vol. 20, pp. 337–344 (2007)

    Google Scholar 

  9. Das, S., Magdon-Ismail, M.: Adapting to a market shock: optimal sequential market-making. In: Koller, D., Bengio, Y., Schuurmans, D., Bottou, L., Culotta, R. (eds.) Advances in Neural Information Processing Systems, Curran Associates, Inc., vol. 21, pp. 361–368 (2008)

    Google Scholar 

  10. DeGroot, M.H.: Optimal Statistical Decisions. Wiley, New York (1970)

    MATH  Google Scholar 

  11. Engelbert, H.J., Shiryaev, A.N.: On absolute continuity and singularity of probability measures. Banach Cent. Publ. 6, 121–132 (1980)

    MathSciNet  Google Scholar 

  12. Garcia-Fernandez, A.F., Svensson, L.: Gaussian MAP filtering using Kalman optimisation. IEEE Trans. Autom. Control, 60(5):1336–1349 (2015)

    Article  MathSciNet  Google Scholar 

  13. Gelman, A., Carlin, J., Stern, H., Rubin, D.: Bayesian Data Analysis, 2nd edn. CRC Press, Boca Raton (2004)

    MATH  Google Scholar 

  14. Gupta, A., Nagar, D.: Matrix Variate Distributions. Chapman & Hall/CRC, London (2000)

    MATH  Google Scholar 

  15. Han, B., Ryzhov, I.O., Defourny, B.: Efficient learning of donor retention strategies for the American Red Cross. In: Pasupathy, R., Kim, S.-H., Tolk, A., Hill, R., Kuhl, M.E. (eds.) Proceedings of the 2013 Winter Simulation Conference, pp. 17–28 (2013)

    Google Scholar 

  16. Herbrich, R., Minka, T.P., Graepel, T.: TrueSkillTM: a Bayesian skill rating system. In: Schölkopf, B., Platt, J.C., Hoffman, T. (eds.) Advances in Neural Information Processing Systems, MIT Press, vol. 19, pp. 569–576 (2006)

    Google Scholar 

  17. Hong, L.J., Nelson, B.L.: A brief introduction to optimization via simulation. In: Rosetti, M., Hill, R., Johansson, B., Dunkin, A., Ingalls, R. (eds.) Proceedings of the 2009 Winter Simulation Conference, pp. 75–85 (2009)

    Google Scholar 

  18. Jaakkola, T.S., Jordan, M.I.: Bayesian parameter estimation via variational methods. Stat. Comput. 10(1), 25–37 (2000)

    Article  Google Scholar 

  19. Kaelbling, L.P.: Learning in Embedded Systems. MIT Press, Cambridge (1993)

    Google Scholar 

  20. Kim, J.-Y.: Limited information likelihood and Bayesian analysis. J. Econom. 107(1), 175–193 (2002)

    Article  MATH  Google Scholar 

  21. Kim, S.: Gradient-based simulation optimization. In: Perrone, L.F., Wieland, F.P., Liu, J., Lawson, B.G., Nicol, D.M., Fujimoto, R.M. (eds.) Proceedings of the 2006 Winter Simulation Conference, pp. 159–167 (2006)

    Google Scholar 

  22. Kushner, H.J., Yin, G.: Stochastic Approximation and Recursive Algorithms and Applications, 2nd edn. Springer, Berlin (2003)

    MATH  Google Scholar 

  23. Marmidis, G., Lazarou, S., Pyrgioti, E.: Optimal placement of wind turbines in a wind park using Monte Carlo simulation. Renew. Energy 33(7), 1455–1460 (2008)

    Article  Google Scholar 

  24. Minka, T.P.: Bayesian linear regression. Technical report, Microsoft Research (2000)

    Google Scholar 

  25. Minka, T.P.: A family of algorithms for approximate Bayesian inference. Ph.D. thesis, Massachusetts Institute of Technology (2001)

    Google Scholar 

  26. Negoescu, D.M., Frazier, P.I., Powell, W.B.: The knowledge-gradient algorithm for sequencing experiments in drug discovery. INFORMS J. Comput. 23(3), 346–363 (2010)

    Article  MathSciNet  Google Scholar 

  27. Pati, D., Bhattacharya, A., Pillai, N.S., Dunson, D.: Posterior contraction in sparse Bayesian factor models for massive covariance matrices. Ann. Stat. 42(3), 1102–1130 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  28. Powell, W.B.: Approximate Dynamic Programming: Solving the Curses of Dimensionality, 2nd edn. Wiley, New York (2011)

    Book  Google Scholar 

  29. Powell, W.B., Ryzhov, I.O.: Optimal Learning. Wiley, New York (2012)

    Book  Google Scholar 

  30. Qu, H., Ryzhov, I.O., Fu, M.C.: Ranking and selection with unknown correlation structures. In: Laroque, C., Himmelspach, J., Pasupathy, R., Rose, O., Uhrmacher, A.M. (eds.) Proceedings of the 2012 Winter Simulation Conference, pp. 144–155 (2012)

    Google Scholar 

  31. Qu, H., Ryzhov, I.O., Fu, M.C.: Learning logistic demand curves in business-to-business pricing. In: Pasupathy, R., Kim, S.-H., Tolk, A., Hill, R., Kuhl, M.E. (eds.) Proceedings of the 2013 Winter Simulation Conference, pp. 29–40 (2013)

    Google Scholar 

  32. Qu, H., Ryzhov, I.O., Fu, M.C., Ding, Z.: Sequential selection with unknown correlation structures. Operations Research, 63(4):931–948 (2015)

    Article  MathSciNet  Google Scholar 

  33. Ryzhov, I.O., Tariq, A., Powell, W.B.: May the best man win: simulation optimization for match-making in e-sports. In: Jain, S., Creasey, R.R., Himmelspach, J., White, K.P., Fu, M.C. (eds.) Proceedings of the 2011 Winter Simulation Conference, pp. 4239–4250 (2011)

    Google Scholar 

  34. Spall, J.C.: Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control. Wiley-Interscience, Hoboken (2005)

    Google Scholar 

  35. Spiegelhalter, D.J., Lauritzen, S.L.: Sequential updating of conditional probabilities on directed graphical structures. Networks 20(5), 579–605 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  36. Talluri, K.T., Van Ryzin, G.J.: The Theory and Practice of Revenue Management. Springer, New York (2006)

    Google Scholar 

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Correspondence to Ilya O. Ryzhov .

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Ryzhov, I.O. (2015). Approximate Bayesian inference for simulation and optimization. In: Defourny, B., Terlaky, T. (eds) Modeling and Optimization: Theory and Applications. Springer Proceedings in Mathematics & Statistics, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-319-23699-5_1

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