While marketing budget allocation has been studied for decades in traditional business, nowadays online business brings much more challenges due to the dynamic environment and complex decision-making process. In this paper, we present a novel unified framework for marketing budget allocation. By leveraging abundant data, the proposed data-driven approach can help us to overcome the challenges and make more informed decisions. In our approach, a semi-black-box model is built to forecast the dynamic market response and an efficient optimization method is proposed to solve the complex allocation task. First, the response in each market-segment is forecasted by exploring historical data through a semi-black-box model, where the capability of logit demand curve is enhanced by neural networks. The response model reveals relationship between sales and marketing cost. Based on the learned model, budget allocation is then formulated as an optimization problem, and we design efficient algorithms to solve it in both continuous and discrete settings. Several kinds of business constraints are supported in one unified optimization paradigm, including cost upper bound, profit lower bound, or ROI lower bound. The proposed framework is easy to implement and readily to handle large-scale problems. It has been successfully applied to many scenarios in Alibaba Group. The results of both offline experiments and online A/B testing demonstrate its effectiveness.

Nonconvex and nonsmooth problems have recently attracted considerable attention in machine learning. However, developing efficient methods for the nonconvex and nonsmooth optimization problems with certain performance guarantee remains a challenge. Proximal coordinate descent (PCD) has been widely used for solving optimization problems, but the knowledge of PCD methods in the nonconvex setting is very limited. On the other hand, the asynchronous proximal coordinate descent (APCD) recently have received much attention in order to solve large-scale problems. However, the accelerated variants of APCD algorithms are rarely studied. In this paper, we extend APCD method to the accelerated algorithm (AAPCD) for nonsmooth and nonconvex problems that satisfies the sufficient descent property, by comparing between the function values at proximal update and a linear extrapolated point using a delay-aware momentum value. To the best of our knowledge, we are the first to provide stochastic and deterministic accelerated extension of APCD algorithms for general nonconvex and nonsmooth problems ensuring that for both bounded delays and unbounded delays every limit point is a critical point. By leveraging Kurdyka-Lojasiewicz property, we will show linear and sublinear convergence rates for the deterministic AAPCD with bounded delays. Numerical results demonstrate the practical efficiency of our algorithm in speed.

Security-Constrained Unit Commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via Mixed-Integer Linear Programming, sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning (ML) techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions and affine subspaces where the optimal solution is likely to lie, leading to significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that, using the proposed techniques, SCUC can be solved on average 12 times faster than conventional methods, with no negative impact on solution quality.

In this work, a unified framework for gradient-free Multidimensional Scaling (MDS) based on Coordinate Search (CS) is proposed. This family of algorithms is an instance of General Pattern Search (GPS) methods which avoid the explicit computation of derivatives but instead evaluate the objective function while searching on coordinate steps of the embedding space. The backbone element of CSMDS framework is the corresponding probability matrix that correspond to how likely is each corresponding coordinate to be evaluated. We propose a Bootstrapped instance of CSMDS (BS CSMDS) which enhances the probability of the direction that decreases the most the objective function while also reducing the corresponding probability of all the other coordinates. BS CSMDS manages to avoid unnecessary function evaluations and result to significant speedup over other CSMDS alternatives while also obtaining the same error rate. Experiments on both synthetic and real data reveal that BS CSMDS performs consistently better than other CSMDS alternatives under various experimental setups.

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the intrinsic non-linear structure of the underlying manifold and the absence of a canonical coordinate system. In machine learning applications, however, most manifolds of interest are represented as matrices with notions of row and column subspaces. In addition, the implicit manifold-related constraints may also lie on such subspaces. For example, the Grassmann manifold is the set of column subspaces. To this end, such a rich structure should not be lost by transforming matrices into just a stack of vectors while developing optimization algorithms on manifolds. We propose novel stochastic gradient algorithms for problems on Riemannian manifolds by adapting the row and column subspaces of gradients. Our algorithms are provably convergent and they achieve the convergence rate of order ${O}(\log (T)/\sqrt{T})$, where $T$ is the number of iterations. Our experiments illustrate that the proposed algorithms outperform existing Riemannian adaptive stochastic algorithms.

Artificial Intelligence has an important place in the scientific community as a result of its successful outputs in terms of different fields. In time, the field of Artificial Intelligence has been divided into many sub-fields because of increasing number of different solution approaches, methods, and techniques. Machine Learning has the most remarkable role with its functions to learn from samples from the environment. On the other hand, intelligent optimization done by inspiring from nature and swarms had its own unique scientific literature, with effective solutions provided for optimization problems from different fields. Because intelligent optimization can be applied in different fields effectively, this study aims to provide a general discussion on multidisciplinary effects of Artificial Intelligence by considering its optimization oriented solutions. The study briefly focuses on background of the intelligent optimization briefly and then gives application examples of intelligent optimization from a multidisciplinary perspective.

Theoretical models of the strong nuclear interaction contain unknown coupling constants (parameters) that must be determined using a pool of calibration data. In cases where the models are complex, leading to time consuming calculations, it is particularly challenging to systematically search the corresponding parameter domain for the best fit to the data. In this paper, we explore the prospect of applying Bayesian optimization to constrain the coupling constants in chiral effective field theory descriptions of the nuclear interaction. We find that Bayesian optimization performs rather well with low-dimensional parameter domains and foresee that it can be particularly useful for optimization of a smaller set of coupling constants. A specific example could be the determination of leading three-nucleon forces using data from finite nuclei or three-nucleon scattering experiments. Bayesian optimization in ab initio nuclear physics 2 1. Introduction Mathematical optimization plays a central role in natural science. Indeed, most theoretical predictions are preceded by a calibration stage whereby the parameters of the model are optimized to reproduce a selected set of calibration data. In nuclear physics, the coupling constants of any theory of the strong interaction between protons and neutrons (nucleons) must be determined from experimental data before one can attempt to solve the Schrödinger equation to make quantitative predictions of the properties of atomic nuclei. Typically, measured low-energy nucleon-nucleon (N N) cross sections and the properties of light nuclei with mass number A 4 have been used for calibrating the NN and three-nucleon (NNN) interaction sectors of the nuclear force, see e.g.

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the available (experimental) degrees of freedom such that more informative measurements are obtained. Unlike the commonly used approaches, which base the OED procedure upon the linearized CRs, we explore a path where we explicitly consider the exact CRs in the OED framework. We use a methodology for a finite parametrization of the exact CRs within the OED problem and we introduce a novel approximation technique of the exact CRs using inner-and outer-approximating ellipsoids as a computationally less demanding alternative. The employed techniques give the OED problem as a finite-dimensional mathematical program of bilevel nature. We use two small-scale illustrative case studies to study various OED criteria and compare the resulting optimal designs with the commonly used linearization-based approach. We also assess the performance of two simple heuristic numerical schemes for bilevel optimization within the studied problems. Introduction At present, advanced industrial engineering and management strive for resource-and energy-efficient design and operation of systems, plants, and processes. Here a use of the model-based techniques is a leading paradigm. The employed models, whether mechanistic or data-based, include a finite number of parameters, whose values are related to the particular natural and system-wide phenomena and are thus commonly only known to belong to some interval or unknown completely.

Projects consist of interconnected dimensions such as objective, time, resource and environment. Use of these dimensions in a controlled way and their effective scheduling brings the project success. Project scheduling process includes defining project activities, and estimation of time and resources to be used for the activities. At this point, the project resource-scheduling problems have begun to attract more attention after Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM) are developed one after the other. However, complexity and difficulty of CPM and PERT processes led to the use of these techniques through artificial intelligence methods such as Genetic Algorithm (GA). In this study, an algorithm was proposed and developed, which determines critical path, critical activities and project completion duration by using GA, instead of CPM and PERT techniques used for network analysis within the scope of project management. The purpose of using GA was that these algorithms are an effective method for solution of complex optimization problems. Therefore, correct decisions can be made for implemented project activities by using obtained results. Thus, optimum results were obtained in a shorter time than the CPM and PERT techniques by using the model based on the dynamic algorithm. It is expected that this study will contribute to the performance field (time, speed, low error etc.) of other studies.

Machine Learning is an important sub-field of the Artificial Intelligence and it has been become a very critical task to train Machine Learning techniques via effective method or techniques. Recently, researchers try to use alternative techniques to improve ability of Machine Learning techniques. Moving from the explanations, objective of this study is to introduce a novel SVM-CoDOA (Cognitive Development Optimization Algorithm trained Support Vector Machines) system for general medical diagnosis. In detail, the system consists of a SVM, which is trained by CoDOA, a newly developed optimization algorithm. As it is known, use of optimization algorithms is an essential task to train and improve Machine Learning techniques. In this sense, the study has provided a medical diagnosis oriented problem scope in order to show effectiveness of the SVM-CoDOA hybrid formation.