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We showcase a variety of functions and classes that implement sampling procedures with improved exploration of the parameter space assisted by machine learning. Special attention is paid to setting sane defaults with the objective that adjustments required by different problems remain minimal. This collection of routines can be employed for different types of analysis, from finding bounds on the parameter space to accumulating samples in areas of interest. In particular, we discuss two methods assisted by incorporating different machine learning models: regression and classification. We show that a machine learning classifier can provide higher efficiency for exploring the parameter space. Also, we introduce a boosting technique to improve the slow convergence at the start of the process. The use of these routines is better explained with the help of a few examples that illustrate the type of results one can obtain. We also include examples of the code used to obtain the examples as well as descriptions of the adjustments that can be made to adapt the calculation to other problems. We finalize by showing the impact of these techniques when exploring the parameter space of the two Higgs doublet model that matches the measured Higgs Boson signal strength. The code used for this paper and instructions on how to use it are available on the web.

Federated learning (FL) is a recently developed area of machine learning, in which the private data of a large number of distributed clients is used to develop a global model under the coordination of a central server without explicitly exposing the data. The standard FL strategy has a number of significant bottlenecks including large communication requirements and high impact on the clients' resources. Several strategies have been described in the literature trying to address these issues. In this paper, a novel scheme based on the notion of "model growing" is proposed. Initially, the server deploys a small model of low complexity, which is trained to capture the data complexity during the initial set of rounds. When the performance of such a model saturates, the server switches to a larger model with the help of function-preserving transformations. The model complexity increases as more data is processed by the clients, and the overall process continues until the desired performance is achieved. Therefore, the most complex model is broadcast only at the final stage in our approach resulting in substantial reduction in communication cost and client computational requirements. The proposed approach is tested extensively on three standard benchmarks and is shown to achieve substantial reduction in communication and client computation while achieving comparable accuracy when compared to the current most effective strategies.

In this paper, a green, quantized FL framework, which represents data with a finite precision level in both local training and uplink transmission, is proposed. Here, the finite precision level is captured through the use of quantized neural networks (QNNs) that quantize weights and activations in fixed-precision format. In the considered FL model, each device trains its QNN and transmits a quantized training result to the base station. Energy models for the local training and the transmission with quantization are rigorously derived. To minimize the energy consumption and the number of communication rounds simultaneously, a multi-objective optimization problem is formulated with respect to the number of local iterations, the number of selected devices, and the precision levels for both local training and transmission while ensuring convergence under a target accuracy constraint. To solve this problem, the convergence rate of the proposed FL system is analytically derived with respect to the system control variables. Then, the Pareto boundary of the problem is characterized to provide efficient solutions using the normal boundary inspection method. Design insights on balancing the tradeoff between the two objectives are drawn from using the Nash bargaining solution and analyzing the derived convergence rate. Simulation results show that the proposed FL framework can reduce energy consumption until convergence by up to 52% compared to a baseline FL algorithm that represents data with full precision.

We examine federated learning (FL) with over-the-air (OTA) aggregation, where mobile users (MUs) aim to reach a consensus on a global model with the help of a parameter server (PS) that aggregates the local gradients. In OTA FL, MUs train their models using local data at every training round and transmit their gradients simultaneously using the same frequency band in an uncoded fashion. Based on the received signal of the superposed gradients, the PS performs a global model update. While the OTA FL has a significantly decreased communication cost, it is susceptible to adverse channel effects and noise. Employing multiple antennas at the receiver side can reduce these effects, yet the path-loss is still a limiting factor for users located far away from the PS. To ameliorate this issue, in this paper, we propose a wireless-based hierarchical FL scheme that uses intermediate servers (ISs) to form clusters at the areas where the MUs are more densely located. Our scheme utilizes OTA cluster aggregations for the communication of the MUs with their corresponding IS, and OTA global aggregations from the ISs to the PS. We present a convergence analysis for the proposed algorithm, and show through numerical evaluations of the derived analytical expressions and experimental results that utilizing ISs results in a faster convergence and a better performance than the OTA FL alone while using less transmit power. We also validate the results on the performance using different number of cluster iterations with different datasets and data distributions. We conclude that the best choice of cluster aggregations depends on the data distribution among the MUs and the clusters.

Federated learning is a data decentralization privacy-preserving technique used to perform machine or deep learning in a secure way. In this paper we present theoretical aspects about federated learning, such as the presentation of an aggregation operator, different types of federated learning, and issues to be taken into account in relation to the distribution of data from the clients, together with the exhaustive analysis of a use case where the number of clients varies. Specifically, a use case of medical image analysis is proposed, using chest X-ray images obtained from an open data repository. In addition to the advantages related to privacy, improvements in predictions (in terms of accuracy and area under the curve) and reduction of execution times will be studied with respect to the classical case (the centralized approach). Different clients will be simulated from the training data, selected in an unbalanced manner, i.e., they do not all have the same number of data. The results of considering three or ten clients are exposed and compared between them and against the centralized case. Two approaches to follow will be analyzed in the case of intermittent clients, as in a real scenario some clients may leave the training, and some new ones may enter the training. The evolution of the results for the test set in terms of accuracy, area under the curve and execution time is shown as the number of clients into which the original data is divided increases. Finally, improvements and future work in the field are proposed.

Federated Learning has been recently proposed for distributed model training at the edge. The principle of this approach is to aggregate models learned on distributed clients to obtain a new more general "average" model (FedAvg). The resulting model is then redistributed to clients for further training. To date, the most popular federated learning algorithm uses coordinate-wise averaging of the model parameters for aggregation. In this paper, we carry out a complete general mathematical convergence analysis to evaluate aggregation strategies in a federated learning framework. From this, we derive novel aggregation algorithms which are able to modify their model architecture by differentiating client contributions according to the value of their losses. Moreover, we go beyond the assumptions introduced in theory, by evaluating the performance of these strategies and by comparing them with the one of FedAvg in classification tasks in both the IID and the Non-IID framework without additional hypothesis.

Federated learning is a data decentralization privacy-preserving technique used to perform machine or deep learning in a secure way. In this paper we present theoretical aspects about federated learning, such as the presentation of an aggregation operator, different types of federated learning, and issues to be taken into account in relation to the distribution of data from the clients, together with the exhaustive analysis of a use case where the number of clients varies. Specifically, a use case of medical image analysis is proposed, using chest X-ray images obtained from an open data repository. In addition to the advantages related to privacy, improvements in predictions (in terms of accuracy and area under the curve) and reduction of execution times will be studied with respect to the classical case (the centralized approach). Different clients will be simulated from the training data, selected in an unbalanced manner, i.e., they do not all have the same number of data. The results of considering three or ten clients are exposed and compared between them and against the centralized case. Two approaches to follow will be analyzed in the case of intermittent clients, as in a real scenario some clients may leave the training, and some new ones may enter the training. The evolution of the results for the test set in terms of accuracy, area under the curve and execution time is shown as the number of clients into which the original data is divided increases. Finally, improvements and future work in the field are proposed.

As a prevalent distributed learning paradigm, Federated Learning (FL) trains a global model on a massive amount of devices with infrequent communication. This paper investigates a class of composite optimization and statistical recovery problems in the FL setting, whose loss function consists of a data-dependent smooth loss and a non-smooth regularizer. Examples include sparse linear regression using Lasso, low-rank matrix recovery using nuclear norm regularization, etc. In the existing literature, federated composite optimization algorithms are designed only from an optimization perspective without any statistical guarantees. In addition, they do not consider commonly used (restricted) strong convexity in statistical recovery problems. We advance the frontiers of this problem from both optimization and statistical perspectives. From optimization upfront, we propose a new algorithm named \textit{Fast Federated Dual Averaging} for strongly convex and smooth loss and establish state-of-the-art iteration and communication complexity in the composite setting. In particular, we prove that it enjoys a fast rate, linear speedup, and reduced communication rounds. From statistical upfront, for restricted strongly convex and smooth loss, we design another algorithm, namely \textit{Multi-stage Federated Dual Averaging}, and prove a high probability complexity bound with linear speedup up to optimal statistical precision. Experiments in both synthetic and real data demonstrate that our methods perform better than other baselines. To the best of our knowledge, this is the first work providing fast optimization algorithms and statistical recovery guarantees for composite problems in FL.

Zeroth-order optimization methods are developed to overcome the practical hurdle of having knowledge of explicit derivatives. Instead, these schemes work with merely access to noisy functions evaluations. The predominant approach is to mimic first-order methods by means of some gradient estimator. The theoretical limitations are well-understood, yet, as most of these methods rely on finite-differencing for shrinking differences, numerical cancellation can be catastrophic. The numerical community developed an efficient method to overcome this by passing to the complex domain. This approach has been recently adopted by the optimization community and in this work we analyze the practically relevant setting of dealing with computational noise. To exemplify the possibilities we focus on the strongly-convex optimization setting and provide a variety of non-asymptotic results, corroborated by numerical experiments, and end with local non-convex optimization.

Deployment of Internet of Things (IoT) devices and Data Fusion techniques have gained popularity in public and government domains. This usually requires capturing and consolidating data from multiple sources. As datasets do not necessarily originate from identical sensors, fused data typically results in a complex data problem. Because military is investigating how heterogeneous IoT devices can aid processes and tasks, we investigate a multi-sensor approach. Moreover, we propose a signal to image encoding approach to transform information (signal) to integrate (fuse) data from IoT wearable devices to an image which is invertible and easier to visualize supporting decision making. Furthermore, we investigate the challenge of enabling an intelligent identification and detection operation and demonstrate the feasibility of the proposed Deep Learning and Anomaly Detection models that can support future application that utilizes hand gesture data from wearable devices.