Neural architecture search (NAS) -- selecting which neural model to use for your learning problem -- is a promising but computationally expensive direction for automating and democratizing machine learning. The weight-sharing method, whose initial success at dramatically accelerating NAS surprised many in the field, has come under scrutiny due to its poor performance as a surrogate for full model-training (a miscorrelation problem known as rank disorder) and inconsistent results on recent benchmarks. In this post, we give a quick overview of weight-sharing and argue in favor of its continued use for NAS. First-generation NAS methods were astronomically expensive due to the combinatorially large search space, requiring the training of thousands of neural networks to completion. Then, in their 2018 ENAS (for Efficient NAS) paper, Pham et al. introduced the idea of weight-sharing, in which only one shared set of model parameters is trained for all architectures.

This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. Again a connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve the problem. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming covering numerical algorithms and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms.

Assortment planning, an important seasonal activity for any retailer, involves choosing the right subset of products to stock in each store.While existing approaches only maximize the expected revenue, we propose including the environmental impact too, through the Higg Material Sustainability Index. The trade-off between revenue and environmental impact is balanced through a multi-objective optimization approach, that yields a Pareto-front of optimal assortments for merchandisers to choose from. Using the proposed approach on a few product categories of a leading fashion retailer shows that choosing assortments with lower environmental impact with a minimal impact on revenue is possible.

A fundamental question in offline reinforcement learning (RL) is how to estimate the value of some target evaluation policy, defined as the long-run average reward obtained by following the policy, using data logged by running a different behavior policy. This question, known as off-policy evaluation (OPE), often arises in applications such as healthcare, education, or robotics, where experimenting with running the target policy can be expensive or even impossible, but we have data logged following business as usual or current standards of care. A central concern using such passively observed data is that observed actions, rewards, and transitions may be confounded by unobserved variables, which can bias standard OPE methods that assume no unobserved confounders, or equivalently that a standard Markov decision process (MDP) model holds with fully observed state. Consider for example evaluating a new smart-phone app to help people living with type-1 diabetes time their insulin injections by monitoring their blood glucose level using some wearable device. Rather than risking giving bad advice that may harm individuals, we may consider first evaluating our injection-timing policy using existing longitudinal observations of individuals' blood glucose levels over time and the timing of insulin injections.

Cloud computing (CC) is a centralized computing paradigm that accumulates resources centrally and provides these resources to users through Internet. Although CC holds a large number of resources, it may not be acceptable by real-time mobile applications, as it is usually far away from users geographically. On the other hand, edge computing (EC), which distributes resources to the network edge, enjoys increasing popularity in the applications with low-latency and high-reliability requirements. EC provides resources in a decentralized manner, which can respond to users' requirements faster than the normal CC, but with limited computing capacities. As both CC and EC are resource-sensitive, several big issues arise, such as how to conduct job scheduling, resource allocation, and task offloading, which significantly influence the performance of the whole system. To tackle these issues, many optimization problems have been formulated. These optimization problems usually have complex properties, such as non-convexity and NP-hardness, which may not be addressed by the traditional convex optimization-based solutions. Computational intelligence (CI), consisting of a set of nature-inspired computational approaches, recently exhibits great potential in addressing these optimization problems in CC and EC. This paper provides an overview of research problems in CC and EC and recent progresses in addressing them with the help of CI techniques. Informative discussions and future research trends are also presented, with the aim of offering insights to the readers and motivating new research directions.

Traditional Chinese medicine (TCM) has played an important role in the prevention and control of the novel coronavirus pneumonia (COVID-19), and community prevention has become the most essential part in reducing the spread risk and protecting populations. However, most communities use a uniform TCM prevention program for all residents, which violates the "treatment based on syndrome differentiation" principle of TCM and limits the effectiveness of prevention. In this paper, we propose an intelligent optimization method to develop diversified TCM prevention programs for community residents. First, we use a fuzzy clustering method to divide the population based on both modern medicine and TCM health characteristics; we then use an interactive optimization method, in which TCM experts develop different TCM prevention programs for different clusters, and a heuristic algorithm is used to optimize the programs under the resource constraints. We demonstrate the computational efficiency of the proposed method and report its successful application to TCM-based prevention of COVID-19 in 12 communities in Zhejiang province, China, during the peak of the pandemic.

Tensor data with rich structural information becomes increasingly important in process modeling, monitoring, and diagnosis. Here structural information is referred to structural properties such as sparsity, smoothness, low-rank, and piecewise constancy. To reveal useful information from tensor data, we propose to decompose the tensor into the summation of multiple components based on different structural information of them. In this paper, we provide a new definition of structural information in tensor data. Based on it, we propose an additive tensor decomposition (ATD) framework to extract useful information from tensor data. This framework specifies a high dimensional optimization problem to obtain the components with distinct structural information. An alternating direction method of multipliers (ADMM) algorithm is proposed to solve it, which is highly parallelable and thus suitable for the proposed optimization problem. Two simulation examples and a real case study in medical image analysis illustrate the versatility and effectiveness of the ATD framework.

This article deals with the sequential design of experiments for (deterministic or stochastic) multi-fidelity numerical simulators, that is, simulators that offer control over the accuracy of simulation of the physical phenomenon or system under study. Very often, accurate simulations correspond to high computational efforts whereas coarse simulations can be obtained at a smaller cost. In this setting, simulation results obtained at several levels of fidelity can be combined in order to estimate quantities of interest (the optimal value of the output, the probability that the output exceeds a given threshold...) in an efficient manner. To do so, we propose a new Bayesian sequential strategy called Maximal Rate of Stepwise Uncertainty Reduction (MR-SUR), that selects additional simulations to be performed by maximizing the ratio between the expected reduction of uncertainty and the cost of simulation. This generic strategy unifies several existing methods, and provides a principled approach to develop new ones. We assess its performance on several examples, including a computationally intensive problem of fire safety analysis where the quantity of interest is the probability of exceeding a tenability threshold during a building fire.

In this paper, we present a novel stochastic optimization method, which uses the binary search technique with first order gradient based optimization method, called Binary Search Gradient Optimization (BSG) or BiGrad. In this optimization setup, a non-convex surface is treated as a set of convex surfaces. In BSG, at first, a region is defined, assuming region is convex. If region is not convex, then the algorithm leaves the region very fast and defines a new one, otherwise, it tries to converge at the optimal point of the region. In BSG, core purpose of binary search is to decide, whether region is convex or not in logarithmic time, whereas, first order gradient based method is primarily applied, to define a new region. In this paper, Adam is used as a first order gradient based method, nevertheless, other methods of this class may also be considered. In deep neural network setup, it handles the problem of vanishing and exploding gradient efficiently. We evaluate BSG on the MNIST handwritten digit, IMDB, and CIFAR10 data set, using logistic regression and deep neural networks. We produce more promising results as compared to other first order gradient based optimization methods. Furthermore, proposed algorithm generalizes significantly better on unseen data as compared to other methods.

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations (PDE) and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, non-convexity, data-sparsity, and non-trivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss-Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to non-quadratic objective functions, most notably, cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In numerical experiments from classification and surrogate modeling, GNvpro not only solves the optimization problem more efficiently but also yields DNNs that generalize better than commonly-used optimization schemes.