Due to the proliferation of smart devices and emerging applications, many next-generation technologies have been paid for the development of wireless networks. Even though commercial 5G has just been widely deployed in some countries, there have been initial efforts from academia and industrial communities for 6G systems. In such a network, a very large number of devices and applications are emerged, along with heterogeneity of technologies, architectures, mobile data, etc., and optimizing such a network is of utmost importance. Besides convex optimization and game theory, swarm intelligence (SI) has recently appeared as a promising optimization tool for wireless networks. As a new subdivision of artificial intelligence, SI is inspired by the collective behaviors of societies of biological species. In SI, simple agents with limited capabilities would achieve intelligent strategies for high-dimensional and challenging problems, so it has recently found many applications in next-generation wireless networks (NGN). However, researchers may not be completely aware of the full potential of SI techniques. In this work, our primary focus will be the integration of these two domains: NGN and SI. Firstly, we provide an overview of SI techniques from fundamental concepts to well-known optimizers. Secondly, we review the applications of SI to settle emerging issues in NGN, including spectrum management and resource allocation, wireless caching and edge computing, network security, and several other miscellaneous issues. Finally, we highlight open challenges and issues in the literature, and introduce some interesting directions for future research.

This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem. We first propose a naive stochastic bandit algorithm for obtaining a probably approximately correct (PAC) solution to this discrete optimization problem in relative precision, that is a solution which solves the optimization problem up to a relative error smaller than a prescribed tolerance, with high probability. We also propose an adaptive stochastic bandit algorithm which provides a PAC-solution with the same guarantees. The adaptive algorithm outperforms the mean complexity of the naive algorithm in terms of number of generated samples and is particularly well suited for applications with high sampling cost.

Sampling from a log-concave distribution function on $\mathbb{R}^d$ (with $d\gg 1$) is a popular problem that has wide applications. In this paper we study the application of random coordinate descent method (RCD) on the Langevin Monte Carlo (LMC) sampling method, and we find two sides of the theory: 1. The direct application of RCD on LMC does reduce the number of finite differencing approximations per iteration, but it induces a large variance error term. More iterations are then needed, and ultimately the method gains no computational advantage; 2. When variance reduction techniques (such as SAGA and SVRG) are incorporated in RCD-LMC, the variance error term is reduced. The new methods, compared to the vanilla LMC, reduce the total computational cost by $d$ folds, and achieve the optimal cost rate. We perform our investigations in both overdamped and underdamped settings.

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type of model with unordered rules, which explains each prediction with a single rule. In order to be easy for humans to understand, these rules must be concise. Earlier work on generating optimal decision sets first minimizes the number of rules, and then minimizes the number of literals, but the resulting rules can often be very large. Here we consider a better measure, namely the total size of the decision set in terms of literals. So we are not driven to a small set of rules which require a large number of literals. We provide the first approach to determine minimum-size decision sets that achieve minimum empirical risk and then investigate sparse alternatives where we trade accuracy for size. By finding optimal solutions we show we can build decision set classifiers that are almost as accurate as the best heuristic methods, but far more concise, and hence more explainable.

We introduce a new incremental preference elicitation procedure able to deal with noisy responses of a Decision Maker (DM). The originality of the contribution is to propose a Bayesian approach for determining a preferred solution in a multiobjective decision problem involving a combinatorial set of alternatives. We assume that the preferences of the DM are represented by an aggregation function whose parameters are unknown and that the uncertainty about them is represented by a density function on the parameter space. Pairwise comparison queries are used to reduce this uncertainty (by Bayesian revision). The query selection strategy is based on the solution of a mixed integer linear program with a combinatorial set of variables and constraints, which requires to use columns and constraints generation methods. Numerical tests are provided to show the practicability of the approach.

This paper introduces an enhanced meta-heuristic (ML-ACO) that combines machine learning (ML) and ant colony optimization (ACO) to solve combinatorial optimization problems. To illustrate the underlying mechanism of our enhanced algorithm, we start by describing a test problem -- the orienteering problem -- used to demonstrate the efficacy of ML-ACO. In this problem, the objective is to find a route that visits a subset of vertices in a graph within a time budget to maximize the collected score. In the first phase of our ML-ACO algorithm, an ML model is trained using a set of small problem instances where the optimal solution is known. Specifically, classification models are used to classify an edge as being part of the optimal route, or not, using problem-specific features and statistical measures. We have tested several classification models including graph neural networks, logistic regression and support vector machines. The trained model is then used to predict the probability that an edge in the graph of a test problem instance belongs to the corresponding optimal route. In the second phase, we incorporate the predicted probabilities into the ACO component of our algorithm. Here, the probability values bias sampling towards favoring those predicted high-quality edges when constructing feasible routes. We empirically show that ML-ACO generates results that are significantly better than the standard ACO algorithm, especially when the computational budget is limited. Furthermore, we show our algorithm is robust in the sense that (a) its overall performance is not sensitive to any particular classification model, and (b) it generalizes well to large and real-world problem instances. Our approach integrating ML with a meta-heuristic is generic and can be applied to a wide range of combinatorial optimization problems.

Feature selection is a data mining task with the potential of speeding up classification algorithms, enhancing model comprehensibility, and improving learning accuracy. However, finding a subset of features that is optimal in terms of predictive accuracy is usually computationally intractable. Out of several heuristic approaches to dealing with this problem, the Recursive Feature Elimination (RFE) algorithm has received considerable interest from data mining practitioners. In this paper, we propose two novel algorithms inspired by RFE, called Fibonacci- and k-Subsecting Recursive Feature Elimination, which remove features in logarithmic steps, probing the wrapped classifier more densely for the more promising feature subsets. The proposed algorithms are experimentally compared against RFE on 28 highly multidimensional datasets and evaluated in a practical case study involving 3D electron density maps from the Protein Data Bank. The results show that Fibonacci and k-Subsecting Recursive Feature Elimination are capable of selecting a smaller subset of features much faster than standard RFE, while achieving comparable predictive performance.

This article provides an overview of Supervised Machine Learning (SML) with a focus on applications to banking. The SML techniques covered include Bagging (Random Forest or RF), Boosting (Gradient Boosting Machine or GBM) and Neural Networks (NNs). We begin with an introduction to ML tasks and techniques. This is followed by a description of: i) tree-based ensemble algorithms including Bagging with RF and Boosting with GBMs, ii) Feedforward NNs, iii) a discussion of hyper-parameter optimization techniques, and iv) machine learning interpretability. The paper concludes with a comparison of the features of different ML algorithms. Examples taken from credit risk modeling in banking are used throughout the paper to illustrate the techniques and interpret the results of the algorithms.

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.