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Distributionally Robust Prescriptive Analytics with Wasserstein Distance [article]

Tianyu Wang, Ningyuan Chen, Chun Wang
2021 arXiv   pre-print
This paper proposes a new distributionally robust approach under Wasserstein ambiguity sets, in which the nominal distribution of Y|X=x is constructed based on the Nadaraya-Watson kernel estimator concerning  ...  We show that the nominal distribution converges to the actual conditional distribution under the Wasserstein distance.  ...  Our Contributions In this paper, we propose a distributionally robust perspective on prescriptive analytics.  ... 
arXiv:2106.05724v1 fatcat:3be5q5wyyzedtcfewtou7bhhki

Distributionally Robust Learning

Ruidi Chen, Ioannis Ch. Paschalidis
2020 Foundations and Trends® in Optimization  
Robust Learning 8.1 Distributionally Robust Learning with Unlabeled Data . . . 8.2 Distributionally Robust Reinforcement Learning . . . . . .  ...  a distance metric weighted by the DRLR solution. • Distributionally Robust Semi-Supervised Learning, which estimates a robust classifier with partially labeled data, through (i) either restricting the  ... 
doi:10.1561/2400000026 fatcat:4urnyh4x3ve33lduoawdqbttmu

Statistical Analysis of Wasserstein Distributionally Robust Estimators [article]

Jose Blanchet and Karthyek Murthy and Viet Anh Nguyen
2021 arXiv   pre-print
The resulting Distributionally Robust Optimization (DRO) formulations, which include Wasserstein DRO formulations (our main focus), are specified using optimal transportation phenomena.  ...  We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems.  ...  In addition, there are burgeoning variants of the optimal transport distance, including the unbalanced optimal transport [23] , subspace robust Wasserstein distance [68] , sliced Wasserstein distance  ... 
arXiv:2108.02120v1 fatcat:dadtqnmvl5bk7phxmqba2aesbi

Distributionally Robust Learning [article]

Ruidi Chen, Ioannis Ch. Paschalidis
2021 arXiv   pre-print
We consider a series of learning problems, including (i) distributionally robust linear regression; (ii) distributionally robust regression with group structure in the predictors; (iii) distributionally  ...  robust multi-output regression and multiclass classification, (iv) optimal decision making that combines distributionally robust regression with nearest-neighbor estimation; (v) distributionally robust  ...  RC is grateful to ICP and David Castañón who have provided constant support and encouragement for her, and have been inspirational role models as excellent researchers and teachers with endless positivity  ... 
arXiv:2108.08993v1 fatcat:6tsadkhvnrgwtk3etkvjumillq

Dynamic optimization with side information [article]

Dimitris Bertsimas, Christopher McCord, Bradley Sturt
2020 arXiv   pre-print
framework uses predictive machine learning methods (such as k-nearest neighbors, kernel regression, and random forests) to weight the relative importance of various data-driven uncertainty sets in a robust  ...  general-purpose approximation for these optimization problems, based on overlapping linear decision rules, which is computationally tractable and produces high-quality solutions for dynamic problems with  ...  the predictive to prescriptive analytics method (PtP-kNN) and sample robust optimization with side information (SRO-kNN).  ... 
arXiv:1907.07307v2 fatcat:i6qvkzkpv5bvpa4prmifqyg6qe

Performance evaluation for distributionally robust optimization with binary entries

Shunichi Ohmori, Kazuho Yoshimoto
2020 An International Journal of Optimization and Control: Theories & Applications  
We applied the distributionally robust optimization technique to minimize the worst-case expected cost taken over the ambiguity set based on the Kullback-Leibler divergence.  ...  We consider the data-driven stochastic programming problem with binary entries where the probability of existence of each entry is not known, instead realization of data is provided.  ...  Bertsimas and van Parys [36] proposed the framework named "bootstrap robust analytics", that integrate distributionally robust optimization and statistical bootstrap that are designed to produce out-ofsamples  ... 
doi:10.11121/ijocta.01.2021.00911 fatcat:vijzbczejndtvm7svkhpnhcwuy

Distributionally Robust Optimization: A Review [article]

Hamed Rahimian, Sanjay Mehrotra
2019 arXiv   pre-print
This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization.  ...  A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities.  ...  By leveraging an analytical formula for the Wasserstein distance between two normal distributions, they obtain an equivalent SDP reformulation of the problem.  ... 
arXiv:1908.05659v1 fatcat:cliwiafz4vffvj2j3b67uix5nm

Consensus Distributionally Robust Optimization with Phi-Divergence

Shunichi Ohmori
2021 IEEE Access  
INDEX TERMS Alternating direction method of multipliers, consensus optimization, decomposition method, distributionally robust optimization, stochastic programming.  ...  We study an efficient algorithm to solve the distributionally robust optimization (DRO) problem, which has recently attracted attention as a new paradigm for decision making in uncertain situations.  ...  Esfahani and Kuhn [3] proposed an ambiguity set that was derived from the Wasserstein distance.  ... 
doi:10.1109/access.2021.3091432 fatcat:cuujkl6mjbcglcw4ofoibwvtsu

A Predictive Prescription Using Minimum Volume k-Nearest Neighbor Enclosing Ellipsoid and Robust Optimization

Shunichi Ohmori
2021 Mathematics  
This paper studies the integration of predictive and prescriptive analytics framework for deriving decision from data.  ...  These have been studied independently, but the effect of the prediction error in predictive analytics on the decision-making in prescriptive analytics has not been clarified.  ...  Esfahani and Kuhn (2018) [29] proposed an ambiguity set derived from the Wasserstein distance.  ... 
doi:10.3390/math9020119 fatcat:uuraqhudc5gjtpbtanqhbf2pau

Distributional Robust Batch Contextual Bandits [article]

Nian Si, Fan Zhang, Zhengyuan Zhou, Jose Blanchet
2022 arXiv   pre-print
In this paper, we lift this assumption and aim to learn a distributionally robust policy with incomplete observational data.  ...  Leveraging this evaluation scheme, we further propose a novel learning algorithm that is able to learn a policy that is robust to adversarial perturbations and unknown covariate shifts with a performance  ...  Taken together, these results highlight that we provide an optimal prescription framework for learning distributionally robust policies.  ... 
arXiv:2006.05630v4 fatcat:o3i2nodt5rf6hiwl7ondoqfl5a

Distributionally robust portfolio maximisation and marginal utility pricing in one period financial markets [article]

Jan Obloj, Johannes Wiesel
2021 arXiv   pre-print
The latter is understood as replacing a baseline model ℙ with an adverse choice from a small Wasserstein ball around ℙ in the space of probability measures.  ...  In this paper we propose to use the Wasserstein distance.  ...  Sensitivity of distributionally robust marginal utility price.  ... 
arXiv:2105.00935v2 fatcat:kx4pvdzxevcrjexz5a2msqmqd4

A General Framework for Optimal Data-Driven Optimization [article]

Tobias Sutter, Bart P.G. Van Parys, Daniel Kuhn
2021 arXiv   pre-print
Our analysis reveals how the structural properties of the data-generating stochastic process impact the shape of the ambiguity set underlying the optimal distributionally robust model.  ...  Hence the optimal method for mapping data to decisions is to solve a distributionally robust optimization model. Maybe surprisingly, this result holds even when the training data is non-i.i.d.  ...  respect to some Wasserstein distance [36, 42] .  ... 
arXiv:2010.06606v2 fatcat:4jfyq7ui6fa6tp65eelvtccld4

Bootstrap Robust Prescriptive Analytics [article]

Dimitris Bertsimas, Bart Van Parys
2021 arXiv   pre-print
When working with noisy or corrupt data, however, such nominal prescriptive methods can be prone to adverse overfitting phenomena and fail to generalize on out-of-sample data.  ...  In this paper we combine ideas from robust optimization and the statistical bootstrap to propose novel prescriptive methods which safeguard against overfitting.  ...  Distributionally Robust Prescriptions with Contextual Information In this paper we extend the distributionally robust optimization perspective to prescription problems with contextual information.  ... 
arXiv:1711.09974v2 fatcat:fmxlonqv7rfpzotdfjty4u5jte

Quantifying Distributional Model Risk via Optimal Transport [article]

Jose Blanchet, Karthyek R. A. Murthy
2017 arXiv   pre-print
These distances, based on optimal transportation between probability measures, include Wasserstein's distances as particular cases.  ...  The proposed methodology is well-suited for risk analysis, as we demonstrate with a number of applications.  ...  The authors would like to thank the anonymous referees whose valuable suggestions have been immensely useful in supplementing the proof of the strong duality theorem with crisp arguments at various instances  ... 
arXiv:1604.01446v2 fatcat:ftk53fcbizgdlp3jynq5jrluqe

Efficient Data-Driven Optimization with Noisy Data [article]

Bart P.G. Van Parys
2022 arXiv   pre-print
Classical Kullback-Leibler or entropic distances have recently been shown to enjoy certain desirable statistical properties in the context of decision-making with noiseless data.  ...  Instead, we study here data-driven prediction problems with data which is corrupted by noise.  ...  In the context of prescriptive analytics such distances have become very popular after the seminal work [17] pointed out that the resulting robust formulation z W,r (P N ) ∈ arg inf z∈Z sup {E P [ (z  ... 
arXiv:2102.04363v2 fatcat:t7t636xh5rfijp5njie4honx7a
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