Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that it uses the same step size (learning rate) for each input variable. This can be a problem on objective functions that have different amounts of curvature in different dimensions, and in turn, may require a different sized step to a new point. Adaptive Gradients, or AdaGrad for short, is an extension of the gradient descent optimization algorithm that allows the step size in each dimension used by the optimization algorithm to be automatically adapted based on the gradients seen for the variable (partial derivatives) seen over the course of the search. In this tutorial, you will discover how to develop the gradient descent with adaptive gradients optimization algorithm from scratch.

Some real problems require the evaluation of expensive and noisy objective functions. Moreover, the analytical expression of these objective functions may be unknown. These functions are known as black-boxes, for example, estimating the generalization error of a machine learning algorithm and computing its prediction time in terms of its hyper-parameters. Multi-objective Bayesian optimization (MOBO) is a set of methods that has been successfully applied for the simultaneous optimization of black-boxes. Concretely, BO methods rely on a probabilistic model of the objective functions, typically a Gaussian process. This model generates a predictive distribution of the objectives. However, MOBO methods have problems when the number of objectives in a multi-objective optimization problem are 3 or more, which is the many objective setting. In particular, the BO process is more costly as more objectives are considered, computing the quality of the solution via the hyper-volume is also more costly and, most importantly, we have to evaluate every objective function, wasting expensive computational, economic or other resources. However, as more objectives are involved in the optimization problem, it is highly probable that some of them are redundant and not add information about the problem solution. A measure that represents how similar are GP predictive distributions is proposed. We also propose a many objective Bayesian optimization algorithm that uses this metric to determine whether two objectives are redundant. The algorithm stops evaluating one of them if the similarity is found, saving resources and not hurting the performance of the multi-objective BO algorithm. We show empirical evidence in a set of toy, synthetic, benchmark and real experiments that GPs predictive distributions of the effectiveness of the metric and the algorithm.

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative observations, however, comes with a dominating $O(N^3D^3)$ computational cost when training on $N$ points in $D$ input dimensions. This is intractable for even moderately sized problems. While recent work has addressed this intractability in the low-$D$ setting, the high-$N$, high-$D$ setting is still unexplored and of great value, particularly as machine learning problems increasingly become high dimensional. In this paper, we introduce methods to achieve fully scalable Gaussian process regression with derivatives using variational inference. Analogous to the use of inducing values to sparsify the labels of a training set, we introduce the concept of inducing directional derivatives to sparsify the partial derivative information of a training set. This enables us to construct a variational posterior that incorporates derivative information but whose size depends neither on the full dataset size $N$ nor the full dimensionality $D$. We demonstrate the full scalability of our approach on a variety of tasks, ranging from a high dimensional stellarator fusion regression task to training graph convolutional neural networks on Pubmed using Bayesian optimization. Surprisingly, we find that our approach can improve regression performance even in settings where only label data is available.

Gaussian process (GP) model based optimization is widely applied in simulation and machine learning. In general, it first estimates a GP model based on a few observations from the true response and then employs this model to guide the search, aiming to quickly locate the global optimum. Despite its successful applications, it has several limitations that may hinder its broader usage. First, building an accurate GP model can be difficult and computationally expensive, especially when the response function is multi-modal or varies significantly over the design space. Second, even with an appropriate model, the search process can be trapped in suboptimal regions before moving to the global optimum due to the excessive effort spent around the current best solution. In this work, we adopt the Additive Global and Local GP (AGLGP) model in the optimization framework. The model is rooted in the inducing-points-based GP sparse approximations and is combined with independent local models in different regions. With these properties, the AGLGP model is suitable for multi-modal responses with relatively large data sizes. Based on this AGLGP model, we propose a Combined Global and Local search for Optimization (CGLO) algorithm. It first divides the whole design space into disjoint local regions and identifies a promising region with the global model. Next, a local model in the selected region is fit to guide detailed search within this region. The algorithm then switches back to the global step when a good local solution is found. The global and local natures of CGLO enable it to enjoy the benefits of both global and local search to efficiently locate the global optimum.

Transfer learning methods aim to produce machine learning models that are trained on a given problem but perform well also on different new tasks. The interest in transfer learning comes from situations where large data sets can be used for solving a given training task but the data associated with new tasks are too small to train expressive models from scratch. The general transfer-learning strategy is to use the small available new data for adapting a large model that has been previously optimized on the training data. One option consists of keeping the structure of the pre-trained large model intact and fine-tuning its weights to solve the new task. When very few data points are available and the pre-trained network is large, however, customized regularization strategies are needed to mitigate the risk of over-fitting. Fine-tuning only a few parameters is a possible way out but can strongly limit the performance of the final model. Another option is to prune the pre-trained model to reduce its complexity, increase transferability, and prevent overfitting. Existing strategies, however, focus on optimized models and are unable to disentangle the network architecture from the attached weights. As a consequence, the pruned version of the original model can hardly be interpreted as a transferable new architecture and it is difficult to reuse it on new tasks.

Shorter product life cycles and increasing individualization of production leads to an increased reconfiguration demand in the domain of industrial automation systems, which will be dominated by cyber-physical production systems in the future. In constantly changing systems, however, not all configuration alternatives of the almost infinite state space are fully understood. Thus, certain configurations can lead to process instability, a reduction in quality or machine failures. Therefore, this paper presents an approach that enhances an intelligent Digital Twin with a self-organized reconfiguration management based on adaptive process models in order to find optimized configurations more comprehensively.

In the context of the introduction of intermittent renewable energies, we propose to optimize the main variables of the control rods of a nuclear power plant to improve its capability to load-follow. The design problem is a black-box combinatorial optimization problem with expensive evaluation based on a multi-physics simulator. Therefore, we use a parallel asynchronous master-worker Evolutionary Algorithm scaling up to thousand computing units. One main issue is the tuning of the algorithm parameters. A fitness landscape analysis is conducted on this expensive real-world problem to show that it would be possible to tune the mutation parameters according to the low-cost estimation of the fitness landscape features.

Agriculture is the foundation of human civilization. However, the rapid increase and aging of the global population pose challenges on this cornerstone by demanding more healthy and fresh food. Internet of Things (IoT) technology makes modern autonomous greenhouse a viable and reliable engine of food production. However, the educated and skilled labor capable of overseeing high-tech greenhouses is scarce. Artificial intelligence (AI) and cloud computing technologies are promising solutions for precision control and high-efficiency production in such controlled environments. In this paper, we propose a smart agriculture solution, namely iGrow: (1) we use IoT and cloud computing technologies to measure, collect, and manage growing data, to support iteration of our decision-making AI module, which consists of an incremental model and an optimization algorithm; (2) we propose a three-stage incremental model based on accumulating data, enabling growers/central computers to schedule control strategies conveniently and at low cost; (3) we propose a model-based iterative optimization algorithm, which can dynamically optimize the greenhouse control strategy in real-time production. In the simulated experiment, evaluation results show the accuracy of our incremental model is comparable to an advanced tomato simulator, while our optimization algorithms can beat the champion of the 2nd Autonomous Greenhouse Challenge. Compelling results from the A/B test in real greenhouses demonstrate that our solution significantly increases production (commercially sellable fruits) (+ 10.15%) and net profit (+ 87.07%) with statistical significance compared to planting experts.

There is significant interest in learning and optimizing a complex system composed of multiple sub-components, where these components may be agents or autonomous sensors. Among the rich literature on this topic, agent-based and domain-specific simulations can capture complex dynamics and subgroup interaction, but optimizing over such simulations can be computationally and algorithmically challenging. Bayesian approaches, such as Gaussian processes (GPs), can be used to learn a computationally tractable approximation to the underlying dynamics but typically neglect the detailed information about subgroups in the complicated system. We attempt to find the best of both worlds by proposing the idea of decomposed feedback, which captures group-based heterogeneity and dynamics. We introduce a novel decomposed GP regression to incorporate the subgroup decomposed feedback. Our modified regression has provably lower variance -- and thus a more accurate posterior -- compared to previous approaches; it also allows us to introduce a decomposed GP-UCB optimization algorithm that leverages subgroup feedback. The Bayesian nature of our method makes the optimization algorithm trackable with a theoretical guarantee on convergence and no-regret property. To demonstrate the wide applicability of this work, we execute our algorithm on two disparate social problems: infectious disease control in a heterogeneous population and allocation of distributed weather sensors. Experimental results show that our new method provides significant improvement compared to the state-of-the-art.

Knowledge distillation uses both real hard labels and soft labels predicted by teacher models as supervision. Intuitively, we expect the soft labels and hard labels to be concordant w.r.t. their orders of probabilities. However, we found critical order violations between hard labels and soft labels in augmented samples. For example, for an augmented sample $x=0.7*panda+0.3*cat$, we expect the order of meaningful soft labels to be $P_\text{soft}(panda|x)>P_\text{soft}(cat|x)>P_\text{soft}(other|x)$. But real soft labels usually violate the order, e.g. $P_\text{soft}(tiger|x)>P_\text{soft}(panda|x)>P_\text{soft}(cat|x)$. We attribute this to the unsatisfactory generalization ability of the teacher, which leads to the prediction error of augmented samples. Empirically, we found the violations are common and injure the knowledge transfer. In this paper, we introduce order restrictions to data augmentation for knowledge distillation, which is denoted as isotonic data augmentation (IDA). We use isotonic regression (IR) -- a classic technique from statistics -- to eliminate the order violations. We show that IDA can be modeled as a tree-structured IR problem. We thereby adapt the classical IRT-BIN algorithm for optimal solutions with $O(c \log c)$ time complexity, where $c$ is the number of labels. In order to further reduce the time complexity, we also propose a GPU-friendly approximation with linear time complexity. We have verified on variant datasets and data augmentation techniques that our proposed IDA algorithms effectively increases the accuracy of knowledge distillation by eliminating the rank violations.