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Residuals-based distributionally robust optimization with covariate information [article]

Rohit Kannan, Güzin Bayraksan, James R. Luedtke
2020 arXiv   pre-print
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
more » ... 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.
arXiv:2012.01088v1 fatcat:sr3fzaoydbg63jomqkgbobuk3q

Sequential sampling for solving stochastic programs

Guzin Bayraksan, David P. Morton
2007 2007 Winter Simulation Conference  
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

Güzin Bayraksan, David P. Morton
2006 Mathematical programming  
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
more » ... 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.
doi:10.1007/s10107-006-0720-x fatcat:vewwlwlyxrduleem5iamkvme5i

A Sequential Sampling Procedure for Stochastic Programming

Güzin Bayraksan, David P. Morton
2011 Operations Research  
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]

Güzin Bayraksan, David P. Morton
2009 Decision Technologies and Applications  
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]

Tito Homem-de-Mello, Güzin Bayraksan
2014 International Series in Operations Research and Management Science  
[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

Brian Keller, Güzin Bayraksan
2012 INFORMS Transactions on Education  
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
more » ... 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.
doi:10.1287/ited.1110.0075ca fatcat:b2kg4mfkkncgdpei76fi7e7ndi

Variance Reduction for Sequential Sampling in Stochastic Programming [article]

Jangho Park and Rebecca Stockbridge and Güzin Bayraksan
2020 arXiv   pre-print
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]

Güzin Bayraksan, David P. Morton, Amit Partani
2010 International Series in Operations Research and Management Science  
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

Brian Keller, GÜzİn Bayraksan
2009 IIE Transactions  
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]

Hamed Rahimian and Guzin Bayraksan and Tito Homem-de-Mello
2021 arXiv   pre-print
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

Güzi̇n Bayraksan, Péguy Pierre-Louis
2012 SIAM Journal on Optimization  
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

David Love, Guzin Bayraksan
2013 2013 Winter Simulations Conference (WSC)  
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

David Love, Guzin Bayraksan
2011 Proceedings of the 2011 Winter Simulation Conference (WSC)  
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]

Jangho Park, Guzin Bayraksan
2020 arXiv   pre-print
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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