scholarly journals From Data to Decisions: Distributionally Robust Optimization Is Optimal

2020 ◽  
Author(s):  
Bart P. G. Van Parys ◽  
Peyman Mohajerin Esfahani ◽  
Daniel Kuhn
Keyword(s):  
Robust Optimization ◽  
Cost Function ◽  
Optimization Problem ◽  
Empirical Distribution ◽  
Distributionally Robust Optimization ◽  
Expected Cost ◽  
Large Deviations Theory ◽  
Out Of Sample ◽  
Distributionally Robust ◽  
Meta Optimization

We study stochastic programs where the decision maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a procedure that transforms the data to an estimate of the expected cost function under the unknown data-generating distribution, that is, a predictor, and an optimizer of the estimated cost function that serves as a near-optimal candidate decision, that is, a prescriptor. As functions of the data, predictors and prescriptors constitute statistical estimators. We propose a meta-optimization problem to find the least conservative predictors and prescriptors subject to constraints on their out-of-sample disappointment. The out-of-sample disappointment quantifies the probability that the actual expected cost of the candidate decision under the unknown true distribution exceeds its predicted cost. Leveraging tools from large deviations theory, we prove that this meta-optimization problem admits a unique solution: The best predictor-prescriptor-pair is obtained by solving a distributionally robust optimization problem over all distributions within a given relative entropy distance from the empirical distribution of the data. This paper was accepted by Chung Piaw Teo, optimization.

scholarly journals Conic reformulations for Kullback-Leibler divergence constrained distributionally robust optimization and applications

2021 ◽  
Vol 11 (2) ◽  
pp. 139-151
Author(s):  
Burak Kocuk
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Empirical Distribution ◽  
Computational Study ◽  
Facility Location Problem ◽  
Optimization Approach ◽  
Distributionally Robust Optimization ◽  
Leibler Divergence ◽  
Distributionally Robust

In this paper, we consider a Kullback-Leibler divergence constrained distributionally robust optimization model. This model considers an ambiguity set that consists of all distributions whose Kullback-Leibler divergence to an empirical distribution is bounded. Utilizing the fact that this divergence measure has an exponential cone representation, we obtain the robust counterpart of the Kullback-Leibler divergence constrained distributionally robust optimization problem as a dual exponential cone constrained program under mild assumptions on the underlying optimization problem. The resulting conic reformulation of the original optimization problem can be directly solved by a commercial conic programming solver. We specialize our generic formulation to two classical optimization problems, namely, the Newsvendor Problem and the Uncapacitated Facility Location Problem. Our computational study in an out-of-sample analysis shows that the solutions obtained via the distributionally robust optimization approach yield significantly better performance in terms of the dispersion of the cost realizations while the central tendency deteriorates only slightly compared to the solutions obtained by stochastic programming.

Optimizing Disruption Tolerance for Rail Transit Networks Under Uncertainty

2021 ◽  
Author(s):  
Lei Xu ◽  
Tsan Sheng (Adam) Ng ◽  
Alberto Costa
Keyword(s):  
Robust Optimization ◽  
Optimization Model ◽  
Optimization Problem ◽  
Mixed Integer ◽  
Rail Transit ◽  
Distributionally Robust Optimization ◽  
Performance Function ◽  
Transit Networks ◽  
Disruption Tolerance ◽  
Distributionally Robust

In this paper, we develop a distributionally robust optimization model for the design of rail transit tactical planning strategies and disruption tolerance enhancement under downtime uncertainty. First, a novel performance function evaluating the rail transit disruption tolerance is proposed. Specifically, the performance function maximizes the worst-case expected downtime that can be tolerated by rail transit networks over a family of probability distributions of random disruption events given a threshold commuter outflow. This tolerance function is then applied to an optimization problem for the planning design of platform downtime protection and bus-bridging services given budget constraints. In particular, our implementation of platform downtime protection strategy relaxes standard assumptions of robust protection made in network fortification and interdiction literature. The resulting optimization problem can be regarded as a special variation of a two-stage distributionally robust optimization model. In order to achieve computational tractability, optimality conditions of the model are identified. This allows us to obtain a linear mixed-integer reformulation that can be solved efficiently by solvers like CPLEX. Finally, we show some insightful results based on the core part of Singapore Mass Rapid Transit Network.

scholarly journals Performance evaluation for distributionally robust optimization with binary entries

2020 ◽  
Vol 11 (1) ◽  
pp. 1-9
Author(s):  
Shunichi Ohmori ◽  
Kazuho Yoshimoto
Keyword(s):  
Performance Evaluation ◽  
Robust Optimization ◽  
Optimization Technique ◽  
Data Driven ◽  
Optimal Decision ◽  
Distributionally Robust Optimization ◽  
Worst Case ◽  
Leibler Divergence ◽  
Out Of Sample ◽  
Distributionally Robust

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. 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 investigate the out-of-sample performance of the resulting optimal decision and analyze its dependence on the sparsity of the problem.

A note on distributionally robust optimization under moment uncertainty

2018 ◽  
Vol 26 (3) ◽  
pp. 141-150
Author(s):  
Qiang Liu ◽  
Jia Wu ◽  
Xiantao Xiao ◽  
Liwei Zhang
Keyword(s):  
Robust Optimization ◽  
Hybrid Method ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Distributionally Robust Optimization ◽  
Support Set ◽  
Whole Space ◽  
The Mean ◽  
Robust Optimization Problem ◽  
Distributionally Robust

AbstractWe considers a distributionally robust optimization problem when the ambiguity set specifies the support as well as the mean and the covariance matrix of the uncertain parameters. After deriving a general deterministic reformulation for the distributionally robust optimization problem, we obtain tractable optimization reformulations when the support set is the whole space and when it is a convex polyhedral set. A hybrid method of Gurobi and a smoothing Newton conjugate gradient method is suggested to solve the tractable optimization problems and numerical results of the hybrid method for solving an illustrative example are reported.

scholarly journals Distributionally Robust Optimization: A review on theory and applications

2022 ◽  
Vol 12 (1) ◽  
pp. 159
Author(s):  
Fengming Lin ◽  
Xiaolei Fang ◽  
Zheming Gao
Keyword(s):  
Robust Optimization ◽  
Operations Research ◽  
Future Research ◽  
Performance Guarantee ◽  
Distributionally Robust Optimization ◽  
Research Directions ◽  
Out Of Sample ◽  
Solution Methods ◽  
Future Research Directions ◽  
Distributionally Robust

<p style='text-indent:20px;'>In this paper, we survey the primary research on the theory and applications of distributionally robust optimization (DRO). We start with reviewing the modeling power and computational attractiveness of DRO approaches, induced by the ambiguity sets structure and tractable robust counterpart reformulations. Next, we summarize the efficient solution methods, out-of-sample performance guarantee, and convergence analysis. Then, we illustrate some applications of DRO in machine learning and operations research, and finally, we discuss the future research directions.</p>

scholarly journals Distributionally robust multi-period portfolio selection subject to bankruptcy constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Lin Jiang ◽  
Changzhi Wu ◽  
Song Wang
Keyword(s):  
Robust Optimization ◽  
Portfolio Selection ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Second Order ◽  
The Other ◽  
Distributionally Robust Optimization ◽  
Second Order Cone ◽  
Robust Optimization Problem ◽  
Distributionally Robust

<p style='text-indent:20px;'>An optimization problem with moments information which suffers from distributional uncertainty can be handled through distributionally robust optimization. In this paper, we will consider distributionally robust multi-period portfolio selection since only moment information of portfolios can be gathered in practice. We will consider two different scenarios. One is that moments information can be obtained exactly and the other one is that the moments information is also uncertain. For the two scenarios, we will show how to transform the corresponding distributionally robust optimization problem into a second order cone problem (SOCP) which can be easily solved by existing methods. Some numerical experiments are presented to demonstrate the effectiveness of our proposed method.</p>

STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH

2021 ◽  
pp. 1-19
Author(s):  
ZUOXUN LI ◽  
KAI ZHANG
Keyword(s):  
Model Predictive Control ◽  
Stochastic Model ◽  
Robust Optimization ◽  
Predictive Control ◽  
Attitude Control ◽  
Optimization Approach ◽  
Distributionally Robust Optimization ◽  
Distributionally Robust ◽  
Stochastic Model Predictive Control ◽  
Rendezvous And Docking

Abstract A stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered during the rendezvous phase. Line-of-sight cone, attitude control bandwidth, and thrust direction constraints are considered during the docking phase. A distributionally robust optimization based algorithm is then proposed by reformulating the SMPC problem into a convex optimization problem. Numerical examples show that the proposed method improves the existing model predictive control based strategy and the robust model predictive control based strategy in the presence of disturbance.

Sign in / Sign up

Export Citation Format

Share Document