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Residuals-based distributionally robust optimization with covariate information
[article]
2020
arXiv
pre-print
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We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of learning setups and DRO ambiguity sets. We investigate the asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within
arXiv:2012.01088v1
fatcat:sr3fzaoydbg63jomqkgbobuk3q
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... our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.
Sequential sampling for solving stochastic programs
2007
2007 Winter Simulation Conference
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We state our results without proof and refer to Bayraksan and Morton (2007) for the proofs. ...
Sufficient conditions for A4 to hold under i.i.d. sampling are given in Bayraksan and Morton (2006) . ...
doi:10.1109/wsc.2007.4419631
dblp:conf/wsc/BayraksanM07
fatcat:ir7xmqgkszguhdcfadshhs2ypm
Assessing solution quality in stochastic programs
2006
Mathematical programming
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Determining whether a solution is of high quality (optimal or near optimal) is fundamental in optimization theory and algorithms. In this paper, we develop Monte Carlo sampling-based procedures for assessing solution quality in stochastic programs. Quality is defined via the optimality gap and our procedures' output is a confidence interval on this gap. We review a multiple-replications procedure that requires solution of, say, 30 optimization problems and then, we present a result that
doi:10.1007/s10107-006-0720-x
fatcat:vewwlwlyxrduleem5iamkvme5i
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... s a computationally simplified singlereplication procedure that only requires solving one optimization problem. Even though the single replication procedure is computationally significantly less demanding, the resulting confidence interval might have low coverage probability for small sample sizes for some problems. We provide variants of this procedure that require two replications instead of one and that perform better empirically. We present computational results for a newsvendor problem and for two-stage stochastic linear programs from the literature. We also discuss when the procedures perform well and when they fail, and we propose using ε-optimal solutions to strengthen the performance of our procedures.
A Sequential Sampling Procedure for Stochastic Programming
2011
Operations Research
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An earlier abbreviated version of this paper appeared in Bayraksan and Morton (2007) . ...
Sufficient conditions for A4 to hold under i.i.d. sampling are given in Bayraksan and Morton (2006) . ...
In Bayraksan and Morton (2006) , we introduced SRP and A2RP and focused on nonsequential estimation involving a single candidate solution,x. ...
doi:10.1287/opre.1110.0926
fatcat:wn4beswnbfgsfnjo4u6un5y5ue
Assessing Solution Quality in Stochastic Programs via Sampling
[chapter]
2009
Decision Technologies and Applications
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For details on this and selection of other parameters; see Bayraksan and Morton [4] . ...
Sufficient conditions to ensure (4) and Theorem 1's proof are provided in Bayraksan and Morton [3] . ...
doi:10.1287/educ.1090.0065
fatcat:6tofe76lpje4bol2n6lrkjfxnu
Stochastic Constraints and Variance Reduction Techniques
[chapter]
2014
International Series in Operations Research and Management Science
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[73] and Mak, Morton, and Wood [64] (we refer the reader to Bayraksan and Morton [7] and Homem-de-Mello and Bayraksan [37] for reviews). The basic idea is as follows. ...
[94] , Homem-de-Mello and Bayraksan [37] and also the chapter by Kim et al. [46] in this book for reviews of that literature. ...
doi:10.1007/978-1-4939-1384-8_9
fatcat:4exjfdng65b7pdywahf7wqu5zm
Case Article—Quantifying Operational Risk in Financial Institutions
2012
INFORMS Transactions on Education
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R isk management is essential in today's business environment for banks and other financial institutions to survive in highly competitive and volatile markets. As the subprime mortgage debacle of 2008 has shown us, risk management, or the lack thereof, affects more than just the individual institution. Hence, banks and other financial institutions are subject to frequent reviews by federal regulators. The regulatory reviews require that the institutions set aside capital (cash reserves) to
doi:10.1287/ited.1110.0075ca
fatcat:b2kg4mfkkncgdpei76fi7e7ndi
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... t the potential risk of loss that they face every day. This case study focuses on a large regional bank, for which we use the pseudonym A Bank, and guides students through developing a risk model for operational risk. The students develop their models using maximum likelihood estimation, goodness-of-fit testing, convolution of distributions, and order statistics. The pedagogical objectives of the case study include applying statistics to a real-world problem while establishing connections among statistics, optimization, and simulation. The case can be used in different disciplines such as engineering (e.g., an engineering statistics class) or business (e.g., a hybrid operations research/statistics MBA class or an elective class on quantitative finance) and for graduate or undergraduate education by changing the intensity of the technical skills required and by using a different mix of case documents.
Variance Reduction for Sequential Sampling in Stochastic Programming
[article]
2020
arXiv
pre-print
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We direct the readers to Homem-de-Mello and Bayraksan [2014 Bayraksan [ , 2015 for further discussion and references on this topic. ...
and Morton, 2006 , Drew, 2007 , Love and Bayraksan, 2015 , Chen et al., 2014 , Stockbridge and Bayraksan, 2013 , Freimer et al., 2012 . ...
arXiv:2005.02458v2
fatcat:sv6g3oht5zhwdgmxvqrwnv34b4
Simulation-Based Optimality Tests for Stochastic Programs
[chapter]
2010
International Series in Operations Research and Management Science
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A version of this chapter appeared in Bayraksan and Morton [6] , with Sections 2-4 and Section 6 largely taken from [6] . ...
This section is based on Bayraksan and Morton [4] , and begins with a single replication procedure to make a valid statistical inference on the quality of a candidate solution. ...
doi:10.1007/978-1-4419-1642-6_3
fatcat:kkiq7ylm6jec7m5v4nrj3kb3fq
Scheduling jobs sharing multiple resources under uncertainty: A stochastic programming approach
2009
IIE Transactions
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See (Bayraksan and Morton, 2008) for more details on the parameters. ...
The rest of the proof is same as in proof of Theorem 3 in (Bayraksan and Morton, 2008) . ...
doi:10.1080/07408170902942683
fatcat:exz2dnh4svfhvpknwm4ut6wpsm
Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance
[article]
2021
arXiv
pre-print
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Our analysis extends the work of Rahimian, Bayraksan, and Homem-de-Mello [Math. Program. 173(1--2): 393--430, 2019], which was in the context of a static/two-stage setting, to the multistage setting. ...
arXiv:2109.06791v1
fatcat:6ybxdtyiy5a5zbwqzv2dvaqiua
Fixed-Width Sequential Stopping Rules for a Class of Stochastic Programs
2012
SIAM Journal on Optimization
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Bayraksan and Morton [3] improve on [31] by relaxing the asymptotic normality assumption and by replacing the unknown variance by a sample variance estimator in the sample size growth conditions. ...
doi:10.1137/090773143
fatcat:646ox7z5qfhxxgjuseunlvkt3e
Two-stage likelihood robust linear program with application to water allocation under uncertainty
2013
2013 Winter Simulations Conference (WSC)
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Parts of this paper also appeared in the Proceedings of the 2013 Industrial and Systems Engineering Research Conference (Love and Bayraksan 2013) . ...
More details on this probability estimation can be found in Love and Bayraksan (2013) . ...
For details on the derivation of optimality and feasibility cuts, see Love and Bayraksan (2013) . ...
doi:10.1109/wsc.2013.6721409
dblp:conf/wsc/LoveB13
fatcat:qc5utyrc5ze7bltqx2lnqlfivq
Overlapping batches for the assessment of solution quality in stochastic programs
2011
Proceedings of the 2011 Winter Simulation Conference (WSC)
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As in Bayraksan and Morton (2006) , the coverage probability of the newsvendor problem drops as m increases. ...
Finally MRP algorithm to these problems presented in Bayraksan and Morton (2006) agree with the results presented here. ...
doi:10.1109/wsc.2011.6148106
dblp:conf/wsc/LoveB11
fatcat:wzpsbbccuzbmljqluv6tqajjau
A Multistage Distributionally Robust Optimization Approach to Water Allocation under Climate Uncertainty
[article]
2020
arXiv
pre-print
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However, not all φ-divergences are capable of suppression, and those that do, can suppress in different ways (Bayraksan and Love, 2015) . ...
Distributionally Robust Optimization (DRO) with φ-divergences in the static/two-stage case has been proposed by the seminal work of Ben-Tal et al. (2013) ; see also further investigations by Bayraksan ...
arXiv:2005.07811v2
fatcat:wmkcrndzdfac3f4wwf3zxqszc4
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