On the Convergence Rates of Expected Improvement Methods

References

• Branke J, Chick SE, Schmidt C (2007) Selecting a selection procedure. Management Sci. 53(12):1916–1932.Link, Google Scholar
• Bull AD (2011) Convergence rates of efficient global optimization algorithms. J. Machine Learn. Res. 12:2879–2904.Google Scholar
• Chau M, Fu MC, Qu H, Ryzhov IO (2014) Simulation optimization: A tutorial overview and recent developments in gradient-based methods. Tolk A, Diallo SY, Ryzhov IO, Yilmaz L, Buckley S, Miller JA, eds. Proc. 2014 Winter Simulation Conf. (IEEE, Piscataway, NJ), 21–35.Crossref, Google Scholar
• Chen CH, Lee LH (2010) Stochastic Simulation Optimization: An Optimal Computing Budget Allocation (World Scientific, Singapore).Crossref, Google Scholar
• Chen CH, Fu MC, Shi L (2008a) Simulation and optimization. Chen ZL, Raghavan S, eds. INFORMS TutORials in Operations Research (INFORMS, Hanover, MD), 247–260.Link, Google Scholar
• Chen CH, Chick SE, Lee LH, Pujowidianto NA (2015) Ranking and selection: Efficient simulation budget allocation. Fu MC, ed. Handbook of Simulation Optimization (Springer, New York), 45–80.Crossref, Google Scholar
• Chen CH, He D, Fu MC, Lee LH (2008b) Efficient simulation budget allocation for selecting an optimal subset. INFORMS J. Comput. 20(4):579–595.Link, Google Scholar
• Chen CH, Lin J, Yücesan E, Chick SE (2000) Simulation budget allocation for further enhancing the efficiency of ordinal optimization. Discrete Event Dynam. Systems 10(3):251–270.Crossref, Google Scholar
• Chick SE (2006) Subjective probability and Bayesian methodology. Henderson SG, Nelson BL, eds. Handbooks in Operations Research and Management Science, Vol. 13: Simulation (North-Holland Publishing, Amsterdam), 225–258.Google Scholar
• Chick SE, Inoue K (2001) New two-stage and sequential procedures for selecting the best simulated system. Oper. Res. 49(5):732–743.Link, Google Scholar
• Chick SE, Branke J, Schmidt C (2010) Sequential sampling to myopically maximize the expected value of information. INFORMS J. Comput. 22(1):71–80.Link, Google Scholar
• DeGroot MH (1970) Optimal Statistical Decisions (McGraw-Hill, New York).Google Scholar
• Finner H, Dickhaus T, Roters M (2008) Asymptotic tail properties of Student’s t-distribution. Comm. Statist.—Theory and Methods 37(2):175–179.Crossref, Google Scholar
• Frazier PI, Powell WB (2010) Paradoxes in learning and the marginal value of information. Decision Anal. 7(4):378–403.Link, Google Scholar
• Frazier PI, Powell WB, Dayanik S (2008) A knowledge gradient policy for sequential information collection. SIAM J. Control Optim. 47(5):2410–2439.Crossref, Google Scholar
• Fu MC, Hu JQ, Chen CH, Xiong X (2007) Simulation allocation for determining the best design in the presence of correlated sampling. INFORMS J. Comput. 19(1):101–111.Link, Google Scholar
• Gao S, Shi L (2014) An optimal opportunity cost selection procedure for a fixed number of designs. Tolk A, Diallo SY, Ryzhov IO, Yilmaz L, Buckley S, Miller JA, eds. Proc. 2014 Winter Simulation Conf. (IEEE, Piscataway, NJ), 2410–2439.Crossref, Google Scholar
• Glynn PW, Juneja S (2004) A large deviations perspective on ordinal optimization. Ingalls R, Rossetti MD, Smith JS, Peters BA, eds. Proc. 2004 Winter Simulation Conf. (IEEE, Piscataway, NJ), 577–585.Crossref, Google Scholar
• Glynn PW, Juneja S (2011) Ordinal optimization: A nonparametric framework. Jain S, Creasey RR, Himmelspach J, White KP, Fu M, eds. Proc. 2011 Winter Simulation Conf. (IEEE, Piscataway, NJ), 4062–4069.Crossref, Google Scholar
• Glynn PW, Juneja S (2015) Ordinal optimization—Empirical large deviations rate estimators, and stochastic multi-armed bandits. arXiv preprint arXiv:1507.04564v1.Google Scholar
• Gupta S, Miescke K (1996) Bayesian look ahead one-stage sampling allocations for selection of the best population. J. Statist. Planning and Inference 54(2):229–244.Crossref, Google Scholar
• Han B, Ryzhov IO, Defourny B (2013) Efficient learning of donor retention strategies for the American Red Cross. Pasupathy R, Kim SH, Tolk A, Hill R, Kuhl ME, eds. Proc. 2013 Winter Simulation Conf. (IEEE, Piscataway, NJ), 17–28.Crossref, Google Scholar
• He D, Chick S, Chen CH (2007) Opportunity cost and OCBA selection procedures in ordinal optimization for a fixed number of alternative systems. IEEE Trans. Systems, Man, and Cybernetics C37(5):951–961.Crossref, Google Scholar
• Hong LJ, Nelson BL (2009) A brief introduction to optimization via simulation. Rosetti M, Hill R, Johansson B, Dunkin A, Ingalls R, eds. Proc. 2009 Winter Simulation Conf. (IEEE, Piscataway, NJ), 75–85.Crossref, Google Scholar
• Jones D, Schonlau M, Welch W (1998) Efficient global optimization of expensive black-box functions. J. Global Optim. 13(4):455–492.Crossref, Google Scholar
• Kim SH, Nelson BL (2006) Selecting the best system. Henderson SG, Nelson BL, eds. Handbooks in Operations Research and Management Science, Vol. 13: Simulation (North-Holland Publishing, Amsterdam), 501–534.Google Scholar
• Kim SH, Nelson BL (2007) Recent advances in ranking and selection. Henderson SG, Biller B, Hsieh MH, Shortle J, Tew JD, Barton RR, eds. Proc. 2007 Winter Simulation Conf. (IEEE, Piscataway, NJ), 162–172.Google Scholar
• Kleinberg J, Tardos É (2006) Algorithm Design (Addison-Wesley, Boston).Google Scholar
• Lai TL, Robbins H (1985) Asymptotically efficient adaptive allocation rules. Adv. Appl. Math. 6:4–22.Crossref, Google Scholar
• Pasupathy R, Hunter SR, Pujowidianto NA, Lee LH, Chen CH (2014) Stochastically constrained ranking and selection via SCORE. ACM Trans. Modeling Comput. Simulation 25(1):1:1–1:26.Crossref, Google Scholar
• Powell WB, Ryzhov IO (2012) Optimal Learning (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
• Qu H, Ryzhov IO, Fu MC, Ding Z (2015) Sequential selection with unknown correlation structures. Oper. Res. 63(4):931–948.Link, Google Scholar
• Russo D, Van Roy B (2014) Learning to optimize via posterior sampling. Math. Oper. Res. 39(4):1221–1243.Link, Google Scholar
• Ryzhov IO (2015) Expected improvement is equivalent to OCBA. Yilmaz L, Chan WKV, Moon I, Roeder TMK, Macal C, Rossetti MD, eds. Proc. 2015 Winter Simulation Conf. (IEEE, Piscataway, NJ), 3668–3677.Crossref, Google Scholar
• Ryzhov IO, Powell WB (2011) Information collection on a graph. Oper. Res. 59(1):188–201.Link, Google Scholar
• Ryzhov IO, Powell WB, Frazier PI (2012) The knowledge gradient algorithm for a general class of online learning problems. Oper. Res. 60(1):180–195.Link, Google Scholar
• Scott WR, Powell WB, Simão HP (2010) Calibrating simulation models using the knowledge gradient with continuous parameters. Johansson B, Jain S, Montoya-Torres J, Hugan J, Yücesan E, eds. Proc. 2010 Winter Simulation Conf. (IEEE, Piscataway, NJ), 1099–1109.Crossref, Google Scholar
• Soms AP (1976) An asymptotic expansion for the tail area of the t-distribution. J. Amer. Statist. Assoc. 71(355):728–730.Google Scholar
• Soms AP (1980) Rational bounds for the t-tail area. J. Amer. Statist. Assoc. 75(370):438–440.Google Scholar
• Szabó B, Tran-Thanh L (2014) On the finite-time analysis of Bayesian online learning algorithms. Submitted for publication.Google Scholar
• Wang Y, Powell WB, Schapire R (2015) Finite-time analysis for the knowledge-gradient policy and a new testing environment for optimal learning. Submitted for publication.Google Scholar