Model Uncertainty, Robust Optimization, and Learning

2006 ◽  
pp. 66-94 ◽  
Author(s):  
Andrew E. B. Lim ◽  
J. George Shanthikumar ◽  
Z. J. Max Shen
Keyword(s):  
Robust Optimization ◽  
Model Uncertainty

Robust Optimization With Mixed Interval and Probabilistic Parameter Uncertainties, Model Uncertainty, and Metamodeling Uncertainty

2019 ◽  
Author(s):  
Yanjun Zhang ◽  
Tingting Xia ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Real World ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Optimization Problems ◽  
Probability Distributions ◽  
Parameter Uncertainties ◽  
True Value ◽  
Uncertainty Model ◽  
The Difference

Abstract Various types of uncertainties, such as parameter uncertainty, model uncertainty, metamodeling uncertainty may lead to low robustness. Parameter uncertainty can be either epistemic or aleatory in physical systems, which have been widely represented by intervals and probability distributions respectively. Model uncertainty is formally defined as the difference between the true value of the real-world process and the code output of the simulation model at the same value of inputs. Additionally, metamodeling uncertainty is introduced due to the usage of metamodels. To reduce the effects of uncertainties, robust optimization (RO) algorithms have been developed to obtain solutions being not only optimal but also less sensitive to uncertainties. Based on how parameter uncertainty is modeled, there are two categories of RO approaches: interval-based and probability-based. In real-world engineering problems, both interval and probabilistic parameter uncertainties are likely to exist simultaneously in a single problem. However, few works have considered mixed interval and probabilistic parameter uncertainties together with other types of uncertainties. In this work, a general RO framework is proposed to deal with mixed interval and probabilistic parameter uncertainties, model uncertainty, and metamodeling uncertainty simultaneously in design optimization problems using the intervals-of-statistics approaches. The consideration of multiple types of uncertainties will improve the robustness of optimal designs and reduce the risk of inappropriate decision-making, low robustness and low reliability in engineering design. Two test examples are utilized to demonstrate the applicability and effectiveness of the proposed RO approach.

Robust Optimization With Parameter and Model Uncertainties Using Gaussian Processes With Limited Samples

2017 ◽  
Author(s):  
Yanjun Zhang ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Engineering Design ◽  
Gaussian Processes ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Computational Cost ◽  
Random Errors ◽  
Model Uncertainties ◽  
Uncertainty Model ◽  
Gp Model

Uncertainty is inevitable in engineering design. The existence of uncertainty may change the optimality and/or the feasibility of the obtained optimal solutions. In simulation-based engineering design, uncertainty could have various types of sources, such as parameter uncertainty, model uncertainty, and other random errors. To deal with uncertainty, robust optimization (RO) algorithms are developed to find solutions which are not only optimal but also robust with respect to uncertainty. Parameter uncertainty has been taken care of by various RO approaches. While model uncertainty has been ignored in majority of existing RO algorithms with the hypothesis that the simulation model used could represent the real physical system perfectly. In the authors’ earlier work, a RO framework was proposed to consider both parameter and model uncertainties using the Bayesian approach with Gaussian processes (GP), where metamodeling uncertainty introduced by GP modeling is ignored by assuming the constructed GP model is accurate enough with sufficient training samples. However, infinite samples are impossible for real applications due to prohibitive time and/or computational cost. In this work, a new RO framework is proposed to deal with both parameter and model uncertainties using GP models but only with limited samples. The compound effect of parameter, model, and metamodeling uncertainties is derived with the form of the compound mean and variance to formulate the proposed RO approach. The proposed RO approach will reduce the risk for the obtained robust optimal designs considering parameter and model uncertainties becoming non-optimal and/or infeasible due to insufficiency of samples for GP modeling. Two test examples with different degrees of complexity are utilized to demonstrate the applicability and effectiveness of the proposed approach.

scholarly journals Distributionally Robust Counterfactual Risk Minimization

2020 ◽  
Vol 34 (04) ◽  
pp. 3850-3857
Author(s):  
Louis Faury ◽  
Ugo Tanielian ◽  
Elvis Dohmatob ◽  
Elena Smirnova ◽  
Flavian Vasile
Keyword(s):  
Decision Making ◽  
Robust Optimization ◽  
Model Uncertainty ◽  
State Of The Art ◽  
Risk Minimization ◽  
Practical Applications ◽  
Uncertainty Measures ◽  
Leibler Divergence ◽  
Benchmark Datasets ◽  
Distributionally Robust

This manuscript introduces the idea of using Distributionally Robust Optimization (DRO) for the Counterfactual Risk Minimization (CRM) problem. Tapping into a rich existing literature, we show that DRO is a principled tool for counterfactual decision making. We also show that well-established solutions to the CRM problem like sample variance penalization schemes are special instances of a more general DRO problem. In this unifying framework, a variety of distributionally robust counterfactual risk estimators can be constructed using various probability distances and divergences as uncertainty measures. We propose the use of Kullback-Leibler divergence as an alternative way to model uncertainty in CRM and derive a new robust counterfactual objective. In our experiments, we show that this approach outperforms the state-of-the-art on four benchmark datasets, validating the relevance of using other uncertainty measures in practical applications.

Using model uncertainty for robust optimization in approximate inference control

2017 ◽  
Vol 22 (3) ◽  
pp. 327-335 ◽  
Author(s):  
Hideaki Itoh ◽  
Yoshitaka Sakai ◽  
Toru Kadoya ◽  
Hisao Fukumoto ◽  
Hiroshi Wakuya ◽  
...  
Keyword(s):  
Robust Optimization ◽  
Model Uncertainty ◽  
Approximate Inference ◽  
Inference Control

Network Congestion Minimization Models Based on Robust Optimization

2018 ◽  
Vol E101.B (3) ◽  
pp. 772-784 ◽  
Author(s):  
Bimal CHANDRA DAS ◽  
Satoshi TAKAHASHI ◽  
Eiji OKI ◽  
Masakazu MURAMATSU
Keyword(s):  
Robust Optimization ◽  
Network Congestion

Risk-Based Robust Bidding Strategies for EVs’ Aggregators in Day-ahead Markets with Uncertainty

2020 ◽  
Author(s):  
Ahmed Abdelmoaty ◽  
Wessam Mesbah ◽  
Mohammad A. M. Abdel-Aal ◽  
Ali T. Alawami
Keyword(s):  
Robust Optimization ◽  
Electricity Market ◽  
Real Life ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Bidding Strategies ◽  
Wind Generators ◽  
Proposed Model ◽  
Optimal Bidding

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual<br>power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy<br>prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO's profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from<br>the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.<br>

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