Data-driven satisficing measure and ranking

We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by Conditional value-at-risk. Starting from offline optimization, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimization case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations).Comment: 26 Pages, 6 Figure

Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical process catalyst. We study a large-scale, industrially-relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pre-trained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models, or they may wish to optimize a discrete model that particularly well-represents a data set. We develop several heuristic methods to find feasible solutions, and an exact, branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on concrete mixture design instance and a chemical catalysis industrial instance

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Beating the index with deep learning:a method for passive investing and systematic active investing

Abstract. In index tracking, while the full replication requires holding all the asset constituents of the index in the tracking portfolio, the sampling approach attempts to construct a tracking portfolio with a subset of assets. Thus, sampling seems to be the approach of choice when considering the flexibility and transaction costs. Two problems that need to be solved to implement the sampling approach are asset selection and asset weighting. This study proposes a framework implemented in two stages: first selecting the assets and then determining asset components’ weights. This study uses a deep autoencoder model for stock selection. The study then applies the L2 regularization technique to set up a quadratic programming problem to determine investment weights of stock components. Since the tracking portfolio tends to underperform the market index after taking management costs into accounts, the portfolio that can generate the excess returns over the index (index beating) brings more competitive advantages to passive fund managers. Thus, the proposed framework attempts to construct a portfolio with a small number of stocks that can both follow the market trends and generate excess returns over the market index. The framework successfully constructed a portfolio with ten stocks beating the S&P 500 index in any given 1-year period with a justifiable risk level

Separable Convex Optimization with Nested Lower and Upper Constraints

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified sampling, support vector machines, portfolio management, and telecommunications. We propose an efficient gradient-free divide-and-conquer algorithm, which uses monotonicity arguments to generate valid bounds from the recursive calls, and eliminate linking constraints based on the information from sub-problems. This algorithm does not need strict convexity or differentiability. It produces an $\epsilon$-approximate solution for the continuous problem in $\mathcal{O}(n \log m \log \frac{n B}{\epsilon})$ time and an integer solution in $\mathcal{O}(n \log m \log B)$ time, where $n$ is the number of decision variables, $m$ is the number of constraints, and $B$ is the resource bound. A complexity of $\mathcal{O}(n \log m)$ is also achieved for the linear and quadratic cases. These are the best complexities known to date for this important problem class. Our experimental analyses confirm the good performance of the method, which produces optimal solutions for problems with up to 1,000,000 variables in a few seconds. Promising applications to the support vector ordinal regression problem are also investigated

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

Adaptive value-at-risk policy optimization: a deep reinforcement learning approach for minimizing the capital charge

In 1995, the Basel Committee on Banking Supervision emitted an amendment to the first Basel Accord, allowing financial institutions to develop internal risk models, based on the value-at-risk (VaR), as opposed to using the regulator’s predefined model. From that point onwards, the scientific community has focused its efforts on improving the accuracy of the VaR models to reduce the capital requirements stipulated by the regulatory framework. In contrast, some authors proposed that the key towards disclosure optimization would not lie in improving the existing models, but in manipulating the estimated value. The most recent progress in this field employed dynamic programming (DP), based on Markov decision processes (MDPs), to create a daily report policy. However, the use of dynamic programming carries heavy costs for the solution; not only does the algorithm require an explicit transition probability matrix, the high computational storage requirements and inability to operate in continuous MDPs demand simplifying the problem. The purpose of this work is to introduce deep reinforcement learning as an alternative to solving problems characterized by a complex or continuous MDP. To this end, the author benchmarks the DP generated policy with one generated via proximal policy optimization. In conclusion, and despite the small number of employed learning iterations, the algorithm showcased a strong convergence with the optimal policy, allowing for the methodology to be used on the unrestricted problem, without incurring in simplifications such as action and state discretization.Em 1995 foi emitida uma adenda ao Acordo de Basileia vigente, o Basileia I, que permitiu que as instituições financeiras optassem por desenvolver modelos internos de medição de risco, tendo por base o value-at-risk (VaR), ao invés de recorrer ao modelo estipulado pelo regulador. Desde então, a comunidade científica focou os seus esforços na melhoria da precisão dos modelos de VaR procurando assim reduzir os requisitos de capital definidos na regulamentação. No entanto, alguns autores propuseram que a chave para a optimização do reporte não estaria na melhoria dos modelos existentes, mas na manipulação do valor estimado. O progresso mais recente recorreu ao uso de programação dinâmica (DP), baseada em processos de decisão de Markov (MDP) para atingir este fim, criando uma regra de reporte diária. No entanto, o uso de DP acarreta custos para a solução, uma vez que por um lado, o algoritmo requer uma matriz de probabilidades de transição definida, e por outro, os elevados requisitos de armazenamento computacional e incapacidade de lidar com processos de decisão de Markov (MDP) contínuos, exigem a simplificação do problema em questão. Este trabalho visa introduzir "deep reinforcement learning" como uma alternativa a problemas caracterizados por um MDP contínuo ou complexo. Para o efeito, é realizado um "benchmarking" com a "policy" criada por programação dinâmica, recorrendo ao algoritmo "proximal policy optimization". Em suma, e apesar do reduzido montante de iterações empregue, o algoritmo demonstrou fortes capacidades de convergência com a solução óptima, podendo ser empregue na estimativa do problema sem incorrer em simplificações