Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure

Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. In this paper we propose an analytic approach to problem-driven scenario generation. This approach applies to stochastic programs where a tail risk measure, such as conditional value-at-risk, is applied to a loss function. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread their scenarios evenly across the support of the random vector, struggle to adequately represent tail risk. Our scenario generation approach works by targeting the construction of scenarios in areas of the distribution corresponding to the tails of the loss distributions. We provide conditions under which our approach is consistent with sampling, and as proof-of-concept demonstrate how our approach could be applied to two classes of problem, namely network design and portfolio selection. Numerical tests on the portfolio selection problem demonstrate that our approach yields better and more stable solutions compared to standard Monte Carlo sampling

Data Mining

The availability of big data due to computerization and automation has generated an urgent need for new techniques to analyze and convert big data into useful information and knowledge. Data mining is a promising and leading-edge technology for mining large volumes of data, looking for hidden information, and aiding knowledge discovery. It can be used for characterization, classification, discrimination, anomaly detection, association, clustering, trend or evolution prediction, and much more in fields such as science, medicine, economics, engineering, computers, and even business analytics. This book presents basic concepts, ideas, and research in data mining

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Inverse Learning: A Data-driven Framework to Infer Optimizations Models

We consider the problem of inferring optimal solutions and unknown parameters of a partially-known constrained problem using a set of past decisions. We assume that the constraints of the original optimization problem are known while optimal decisions and the objective are to be inferred. In such situations, the quality of the optimal solution is evaluated in relation to the existing observations and the known parameters of the constrained problem. A method previously used in such settings is inverse optimization. This method can be used to infer the utility functions of a decision-maker and to find optimal solutions based on these inferred parameters indirectly. However, little effort has been made to generalize the inverse optimization methodology to data-driven settings to address the quality of the inferred optimal solutions. In this work, we present a data-driven inverse linear optimization framework (Inverse Learning) that aims to infer the optimal solution to an optimization problem directly based on the observed data and the existing known parameters of the problem. We validate our model on a dataset in the diet recommendation problem setting to find personalized diets for prediabetic patients with hypertension. Our results show that our model obtains optimal personalized daily food intakes that preserve the original data trends while providing a range of options to patients and providers. The results show that our proposed model is able to both capture optimal solutions with minimal perturbation from the given observations and, at the same time, achieve the inherent objectives of the original problem. We show an inherent trade-off in the quality of the inferred solutions with different metrics and provide insights into how a range of optimal solutions can be inferred in constrained environments