Unsupervised Learning and Robust Optimization in the Portfolio Problem

2020 ◽  
pp. 4-9
Author(s):  
Grigorii I. Beliavsky ◽  
Natalia V. Danilova ◽  
Alexey D. Logunov
Keyword(s):  
Machine Learning ◽  
Decision Making ◽  
Robust Optimization ◽  
Unsupervised Learning ◽  
Optimization Problem ◽  
Clustering Algorithm ◽  
Learning Problems ◽  
Portfolio Problem ◽  
Robust Optimization Problem ◽  
Decision Making Model

Robust optimization in various problems of science and technology arises from the uncertainty of the parameters that determine the decision-making model. The parameters can be judged on the basis of a large number of observed examples. This challenge is to customize a solution based on a large number of examples that works well for examples that were not involved in customizing the solution. In this sense, the robust optimization problem belongs to machine learning problems. The paper uses a dichotomous clustering algorithm to determine the range of parameters for the optimal portfolio problem.

Application of Machine Learning in Animal Disease Analysis and Prediction

2020 ◽  
Vol 15 ◽  
Author(s):  
Shuwen Zhang ◽  
Qiang Su ◽  
Qin Chen
Keyword(s):  
Machine Learning ◽  
Unsupervised Learning ◽  
Supervised Learning ◽  
Clustering Algorithm ◽  
Principal Component ◽  
Support Vector ◽  
Animal Disease ◽  
Human Beings ◽  
Animal Diseases ◽  
Disease Analysis

Abstract: Major animal diseases pose a great threat to animal husbandry and human beings. With the deepening of globalization and the abundance of data resources, the prediction and analysis of animal diseases by using big data are becoming more and more important. The focus of machine learning is to make computers learn how to learn from data and use the learned experience to analyze and predict. Firstly, this paper introduces the animal epidemic situation and machine learning. Then it briefly introduces the application of machine learning in animal disease analysis and prediction. Machine learning is mainly divided into supervised learning and unsupervised learning. Supervised learning includes support vector machines, naive bayes, decision trees, random forests, logistic regression, artificial neural networks, deep learning, and AdaBoost. Unsupervised learning has maximum expectation algorithm, principal component analysis hierarchical clustering algorithm and maxent. Through the discussion of this paper, people have a clearer concept of machine learning and understand its application prospect in animal diseases.

Toward the Use of Pareto Performance Solutions and Pareto Robustness Solutions for Multi-Objective Robust Optimization Problems

2012 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis ◽  
Oscar Brito Augusto
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Robust Solutions ◽  
Multi Objective ◽  
Robust Optimization Problem ◽  
Design Solutions ◽  
Further Development

For Multi-Objective Robust Optimization Problem (MOROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a MOROP into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions (PP) and the Pareto Robustness Solutions (PR). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions (PR(PP)), and the Pareto Performance Solutions among the Pareto Robustness Solutions (PP(PR)). Further more, the intersection of PR(PP) and PP(PR) can represent the intersection of PR and PP well. Then the designer can choose good solutions by comparing the results of PR(PP) and PP(PR). Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.

scholarly journals On the Optimality of Affine Policies for Budgeted Uncertainty Sets

2021 ◽  
Author(s):  
Omar El Housni ◽  
Vineet Goyal
Keyword(s):  
Robust Optimization ◽  
Structural Properties ◽  
Optimization Problem ◽  
Hardness Of Approximation ◽  
Uncertain Parameters ◽  
Two Stage ◽  
Uncertainty Sets ◽  
Adjustable Robust Optimization ◽  
Robust Optimization Problem ◽  
Budgeted Uncertainty

In this paper, we study the performance of affine policies for a two-stage, adjustable, robust optimization problem with a fixed recourse and an uncertain right-hand side belonging to a budgeted uncertainty set. This is an important class of uncertainty sets, widely used in practice, in which we can specify a budget on the adversarial deviations of the uncertain parameters from the nominal values to adjust the level of conservatism. The two-stage adjustable robust optimization problem is hard to approximate within a factor better than [Formula: see text] even for budget of uncertainty sets in which [Formula: see text] is the number of decision variables. Affine policies, in which the second-stage decisions are constrained to be an affine function of the uncertain parameters provide a tractable approximation for the problem and have been observed to exhibit good empirical performance. We show that affine policies give an [Formula: see text]-approximation for the two-stage, adjustable, robust problem with fixed nonnegative recourse for budgeted uncertainty sets. This matches the hardness of approximation, and therefore, surprisingly, affine policies provide an optimal approximation for the problem (up to a constant factor). We also show strong theoretical performance bounds for affine policy for a significantly more general class of intersection of budgeted sets, including disjoint constrained budgeted sets, permutation invariant sets, and general intersection of budgeted sets. Our analysis relies on showing the existence of a near-optimal, feasible affine policy that satisfies certain nice structural properties. Based on these structural properties, we also present an alternate algorithm to compute a near-optimal affine solution that is significantly faster than computing the optimal affine policy by solving a large linear program.

scholarly journals Robust Optimization for Electricity Generation

2020 ◽  
Author(s):  
Haoxiang Yang ◽  
David P. Morton ◽  
Chaithanya Bandi ◽  
Krishnamurthy Dvijotham
Keyword(s):  
Renewable Energy ◽  
Robust Optimization ◽  
Electric Power ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimization Problem ◽  
Convex Relaxation ◽  
Electric Power System ◽  
Robust Convex Optimization ◽  
Robust Optimization Problem

We consider a robust optimization problem in an electric power system under uncertain demand and availability of renewable energy resources. Solving the deterministic alternating current (AC) optimal power flow (ACOPF) problem has been considered challenging since the 1960s due to its nonconvexity. Linear approximation of the AC power flow system sees pervasive use, but does not guarantee a physically feasible system configuration. In recent years, various convex relaxation schemes for the ACOPF problem have been investigated, and under some assumptions, a physically feasible solution can be recovered. Based on these convex relaxations, we construct a robust convex optimization problem with recourse to solve for optimal controllable injections (fossil fuel, nuclear, etc.) in electric power systems under uncertainty (renewable energy generation, demand fluctuation, etc.). We propose a cutting-plane method to solve this robust optimization problem, and we establish convergence and other desirable properties. Experimental results indicate that our robust convex relaxation of the ACOPF problem can provide a tight lower bound.

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

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 119
Author(s):  
Shunichi Ohmori
Keyword(s):  
Machine Learning ◽  
Decision Making ◽  
Robust Optimization ◽  
Nearest Neighbor ◽  
Predictive Analytics ◽  
Uncertain Parameters ◽  
Minimum Volume ◽  
K Nearest Neighbor ◽  
Modeling Framework ◽  
Prescriptive Analytics

This paper studies the integration of predictive and prescriptive analytics framework for deriving decision from data. Traditionally, in predictive analytics, the purpose is to derive prediction of unknown parameters from data using statistics and machine learning, and in prescriptive analytics, the purpose is to derive a decision from known parameters using optimization technology. 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. We propose a modeling framework that integrates machine learning and robust optimization. The proposed algorithm utilizes the k-nearest neighbor model to predict the distribution of uncertain parameters based on the observed auxiliary data. The enclosing minimum volume ellipsoid that contains k-nearest neighbors of is used to form the uncertainty set for the robust optimization formulation. We illustrate the data-driven decision-making framework and our novel robustness notion on a two-stage linear stochastic programming under uncertain parameters. The problem can be reduced to a convex programming, and thus can be solved to optimality very efficiently by the off-the-shelf solvers.

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