In this paper we describe a parameterized family of first-order distributed optimization algorithms that enable a network of agents to collaboratively calculate a decision variable that minimizes the sum of cost functions at each agent. These algorithms are self-healing in that their correctness is guaranteed even if they are initialized randomly, agents drop in or out of the network, local cost functions change, or communication packets are dropped. Our algorithms are the first single-Laplacian methods to exhibit all of these characteristics. We achieve self-healing by sacrificing internal stability, a fundamental trade-off for single-Laplacian methods.

Variational inference is a popular alternative to Markov chain Monte Carlo methods that constructs a Bayesian posterior approximation by minimizing a discrepancy to the true posterior within a pre-specified family. This converts Bayesian inference into an optimization problem, enabling the use of simple and scalable stochastic optimization algorithms. However, a key limitation of variational inference is that the optimal approximation is typically not tractable to compute; even in simple settings the problem is nonconvex. Thus, recently developed statistical guarantees -- which all involve the (data) asymptotic properties of the optimal variational distribution -- are not reliably obtained in practice. In this work, we provide two major contributions: a theoretical analysis of the asymptotic convexity properties of variational inference in the popular setting with a Gaussian family; and consistent stochastic variational inference (CSVI), an algorithm that exploits these properties to find the optimal approximation in the asymptotic regime. CSVI consists of a tractable initialization procedure that finds the local basin of the optimal solution, and a scaled gradient descent algorithm that stays locally confined to that basin. Experiments on nonconvex synthetic and real-data examples show that compared with standard stochastic gradient descent, CSVI improves the likelihood of obtaining the globally optimal posterior approximation.

A broad class of unsupervised deep learning methods such as Generative Adversarial Networks (GANs) involve training of overparameterized models where the number of parameters of the model exceeds a certain threshold. Indeed, most successful GANs used in practice are trained using overparameterized generator and discriminator networks, both in terms of depth and width. A large body of work in supervised learning have shown the importance of model overparameterization in the convergence of the gradient descent (GD) to globally optimal solutions. In contrast, the unsupervised setting and GANs in particular involve non-convex concave mini-max optimization problems that are often trained using Gradient Descent/Ascent (GDA). The role and benefits of model overparameterization in the convergence of GDA to a global saddle point in non-convex concave problems is far less understood. In this work, we present a comprehensive analysis of the importance of model overparameterization in GANs both theoretically and empirically. We theoretically show that in an overparameterized GAN model with a 1-layer neural network generator and a linear discriminator, GDA converges to a global saddle point of the underlying non-convex concave min-max problem. To the best of our knowledge, this is the first result for global convergence of GDA in such settings. Our theory is based on a more general result that holds for a broader class of nonlinear generators and discriminators that obey certain assumptions (including deeper generators and random feature discriminators). Our theory utilizes and builds upon a novel connection with the convergence analysis of linear timevarying dynamical systems which may have broader implications for understanding the convergence behavior of GDA for non-convex concave problems involving overparameterized models. We also empirically study the role of model overparameterization in GANs using several large-scale experiments on CIFAR-10 and Celeb-A datasets.

B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto sets/fronts when sample points exactly lie on the Pareto set/front. However, if the sample points scatter away from the Pareto set/front, those methods often likely suffer from over-fitting. To overcome this issue, in this paper, we extend the B\'ezier simplex model to a probabilistic one and propose a new learning algorithm of it, which falls into the framework of approximate Bayesian computation (ABC) based on the Wasserstein distance. We also study the convergence property of the Wasserstein ABC algorithm. An extensive experimental evaluation on publicly available problem instances shows that the new algorithm converges on a finite sample. Moreover, it outperforms the deterministic fitting methods on noisy instances.

In 2019, Anderson et al. proposed the concept of rankability, which refers to a dataset's inherent ability to be meaningfully ranked. In this article, we give an expository review of the linear ordering problem (LOP) and then use it to analyze the rankability of data. Specifically, the degree of linearity is used to quantify what percentage of the data aligns with an optimal ranking. In a sports context, this is analogous to the number of games that a ranking can correctly predict in hindsight. In fact, under the appropriate objective function, we show that the optimal rankings computed via the LOP maximize the hindsight accuracy of a ranking. Moreover, we develop a binary program to compute the maximal Kendall tau ranking distance between two optimal rankings, which can be used to measure the diversity among optimal rankings without having to enumerate all optima. Finally, we provide several examples from the world of sports and college rankings to illustrate these concepts and demonstrate our results.

We consider the problem of sequentially allocating resources in a censored semi-bandits setup, where the learner allocates resources at each step to the arms and observes loss. The loss depends on two hidden parameters, one specific to the arm but independent of the resource allocation, and the other depends on the allocated resource. More specifically, the loss equals zero for an arm if the resource allocated to it exceeds a constant (but unknown) arm dependent threshold. The goal is to learn a resource allocation that minimizes the expected loss. The problem is challenging because the loss distribution and threshold value of each arm are unknown. We study this setting by establishing its `equivalence' to Multiple-Play Multi-Armed Bandits (MP-MAB) and Combinatorial Semi-Bandits. Exploiting these equivalences, we derive optimal algorithms for our problem setting using known algorithms for MP-MAB and Combinatorial Semi-Bandits. The experiments on synthetically generated data validate the performance guarantees of the proposed algorithms.

Counterfactuals have become a popular technique nowadays for interacting with black-box machine learning models and understanding how to change a particular instance to obtain a desired outcome from the model. However, most existing approaches assume instant materialization of these changes, ignoring that they may require effort and a specific order of application. Recently, methods have been proposed that also consider the order in which actions are applied, leading to the so-called sequential counterfactual generation problem. In this work, we propose a model-agnostic method for sequential counterfactual generation. We formulate the task as a multi-objective optimization problem and present an evolutionary approach to find optimal sequences of actions leading to the counterfactuals. Our cost model considers not only the direct effect of an action, but also its consequences. Experimental results show that compared to state of the art, our approach generates less costly solutions, is more efficient, and provides the user with a diverse set of solutions to choose from.

The paper focuses on the a posteriori tuning of a generative model in order to favor the generation of good instances in the sense of some external differentiable criterion. The proposed approach, called Boltzmann Tuning of Generative Models (BTGM), applies to a wide range of applications. It covers conditional generative modelling as a particular case, and offers an affordable alternative to rejection sampling. The contribution of the paper is twofold. Firstly, the objective is formalized and tackled as a well-posed optimization problem; a practical methodology is proposed to choose among the candidate criteria representing the same goal, the one best suited to efficiently learn a tuned generative model. Secondly, the merits of the approach are demonstrated on a real-world application, in the context of robust design for energy policies, showing the ability of BTGM to sample the extreme regions of the considered criteria.

Machine Learning (ML) techniques are becoming an invaluable support for network intrusion detection, especially in revealing anomalous flows, which often hide cyber-threats. Typically, ML algorithms are exploited to classify/recognize data traffic on the basis of statistical features such as inter-arrival times, packets length distribution, mean number of flows, etc. Dealing with the vast diversity and number of features that typically characterize data traffic is a hard problem. This results in the following issues: i) the presence of so many features leads to lengthy training processes (particularly when features are highly correlated), while prediction accuracy does not proportionally improve; ii) some of the features may introduce bias during the classification process, particularly those that have scarce relation with the data traffic to be classified. To this end, by reducing the feature space and retaining only the most significant features, Feature Selection (FS) becomes a crucial pre-processing step in network management and, specifically, for the purposes of network intrusion detection. In this review paper, we complement other surveys in multiple ways: i) evaluating more recent datasets (updated w.r.t. obsolete KDD 99) by means of a designed-from-scratch Python-based procedure; ii) providing a synopsis of most credited FS approaches in the field of intrusion detection, including Multi-Objective Evolutionary techniques; iii) assessing various experimental analyses such as feature correlation, time complexity, and performance. Our comparisons offer useful guidelines to network/security managers who are considering the incorporation of ML concepts into network intrusion detection, where trade-offs between performance and resource consumption are crucial.

System design tools are often only available as blackboxes with complex nonlinear relationships between inputs and outputs. Blackboxes typically run in the forward direction: for a given design as input they compute an output representing system behavior. Most cannot be run in reverse to produce an input from requirements on output. Thus, finding a design satisfying a requirement is often a trial-and-error process without assurance of optimality. Finding designs concurrently satisfying multiple requirements is harder because designs satisfying individual requirements may conflict with each other. Compounding the hardness are the facts that blackbox evaluations can be expensive and sometimes fail to produce an output due to non-convergence of underlying numerical algorithms. This paper presents CNMA (Constrained optimization with Neural networks, MILP solvers and Active Learning), a new optimization method for blackboxes. It is conservative in the number of blackbox evaluations. Any designs it finds are guaranteed to satisfy all requirements. It is resilient to the failure of blackboxes to compute outputs. It tries to sample only the part of the design space relevant to solving the design problem, leveraging the power of neural networks, MILPs, and a new learning-from-failure feedback loop. The paper also presents parallel CNMA that improves the efficiency and quality of solutions over the sequential version, and tries to steer it away from local optima. CNMA's performance is evaluated for seven nonlinear design problems of 8 (2 problems), 10, 15, 36 and 60 real-valued dimensions and one with 186 binary dimensions. It is shown that CNMA improves the performance of stable, off-the-shelf implementations of Bayesian Optimization and Nelder Mead and Random Search by 1%-87% for a given fixed time and function evaluation budget. Note, that these implementations did not always return solutions.