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We propose a test procedure to compare simultaneously $K$ copulas, with $K \geq 2$. The $K$ observed populations can be paired. The test statistic is based on the differences between orthogonal projection coefficients associated to the density copulas, that we called {\it copula coefficients}. The procedure is data driven and we obtain a chi-square asymptotic distribution of the test statistic under the null. We illustrate our procedure via numerical studies and through two real datasets. Eventually, a clustering algorithm is deduced from the $K$-sample test and its performances are illustrated in a simulation experiment.

Gradient descent ascent (GDA), the simplest single-loop algorithm for nonconvex minimax optimization, is widely used in practical applications such as generative adversarial networks (GANs) and adversarial training. Albeit its desirable simplicity, recent work shows inferior convergence rates of GDA in theory even assuming strong concavity of the objective on one side. This paper establishes new convergence results for two alternative single-loop algorithms -- alternating GDA and smoothed GDA -- under the mild assumption that the objective satisfies the Polyak-Lojasiewicz (PL) condition about one variable. We prove that, to find an $\epsilon$-stationary point, (i) alternating GDA and its stochastic variant (without mini batch) respectively require $O(\kappa^{2} \epsilon^{-2})$ and $O(\kappa^{4} \epsilon^{-4})$ iterations, while (ii) smoothed GDA and its stochastic variant (without mini batch) respectively require $O(\kappa \epsilon^{-2})$ and $O(\kappa^{2} \epsilon^{-4})$ iterations. The latter greatly improves over the vanilla GDA and gives the hitherto best known complexity results among single-loop algorithms under similar settings. We further showcase the empirical efficiency of these algorithms in training GANs and robust nonlinear regression.

Safe autonomous navigation in unknown environments is an important problem for ground, aerial, and underwater robots. This paper proposes techniques to learn the dynamics models of a mobile robot from trajectory data and synthesize a tracking controller with safety and stability guarantees. The state of a mobile robot usually contains its position, orientation, and generalized velocity and satisfies Hamilton's equations of motion. Instead of a hand-derived dynamics model, we use a dataset of state-control trajectories to train a translation-equivariant nonlinear Hamiltonian model represented as a neural ordinary differential equation (ODE) network. The learned Hamiltonian model is used to synthesize an energy-shaping passivity-based controller and derive conditions which guarantee safe regulation to a desired reference pose. Finally, we enable adaptive tracking of a desired path, subject to safety constraints obtained from obstacle distance measurements. The trade-off between the system's energy level and the distance to safety constraint violation is used to adaptively govern the reference pose along the desired path. Our safe adaptive controller is demonstrated on a simulated hexarotor robot navigating in unknown complex environments.

Security has become paramount in modern software services as more and more security breaches emerge, impacting final users and organizations alike. Trends like the Microservice Architecture bring new security challenges related to communication, system design, development, and operation. The literature presents a plethora of security-related solutions for microservices-based systems, but the spread of information difficult practitioners' adoption of novel security related solutions. In this study, we aim to present a catalogue and discussion of security solutions based on algorithms, protocols, standards, or implementations; supporting principles or characteristics of information security, considering the three possible states of data, according to the McCumber Cube. Our research follows a Systematic Literature Review, synthesizing the results with a meta-aggregation process. We identified a total of 30 primary studies, yielding 75 security solutions for the communication of microservices.

The recent MSMARCO passage retrieval collection has allowed researchers to develop highly tuned retrieval systems. One aspect of this data set that makes it distinctive compared to traditional corpora is that most of the topics only have a single answer passage marked relevant. Here we carry out a "what if" sensitivity study, asking whether a set of systems would still have the same relative performance if more passages per topic were deemed to be "relevant", exploring several mechanisms for identifying sets of passages to be so categorized. Our results show that, in general, while run scores can vary markedly if additional plausible passages are presumed to be relevant, the derived system ordering is relatively insensitive to additional relevance, providing support for the methodology that was used at the time the MSMARCO passage collection was created.

Multi-agent reinforcement learning (MARL) has attracted much research attention recently. However, unlike its single-agent counterpart, many theoretical and algorithmic aspects of MARL have not been well-understood. In this paper, we study the emergence of coordinated behavior by autonomous agents using an actor-critic (AC) algorithm. Specifically, we propose and analyze a class of coordinated actor-critic algorithms (CAC) in which individually parametrized policies have a {\it shared} part (which is jointly optimized among all agents) and a {\it personalized} part (which is only locally optimized). Such kind of {\it partially personalized} policy allows agents to learn to coordinate by leveraging peers' past experience and adapt to individual tasks. The flexibility in our design allows the proposed MARL-CAC algorithm to be used in a {\it fully decentralized} setting, where the agents can only communicate with their neighbors, as well as a {\it federated} setting, where the agents occasionally communicate with a server while optimizing their (partially personalized) local models. Theoretically, we show that under some standard regularity assumptions, the proposed MARL-CAC algorithm requires $\mathcal{O}(\epsilon^{-\frac{5}{2}})$ samples to achieve an $\epsilon$-stationary solution (defined as the solution whose squared norm of the gradient of the objective function is less than $\epsilon$). To the best of our knowledge, this work provides the first finite-sample guarantee for decentralized AC algorithm with partially personalized policies.

Understanding the underlying causes of maternal death across all regions of the world is essential to inform policies and resource allocation to reduce the mortality burden. However, in many countries of the world there exists very little data on the causes of maternal death, and data that do exist do not capture the entire population of risk. In this paper we present a Bayesian hierarchical multinomial model to estimate maternal cause of death distributions globally, regionally and for all countries worldwide. The framework combines data from various sources to inform estimates, including data from civil registration and vital systems, smaller-scale surveys and studies, and high-quality data from confidential enquiries and surveillance systems. The framework accounts of varying data quality and coverage, and allows for situations where one or more causes of death are missing. We illustrate the results of the model on three case study countries that have different data availability situations.

The essence of distributed computing systems is how to schedule incoming requests and how to allocate all computing nodes to minimize both time and computation costs. In this paper, we propose a cost-aware optimal scheduling and allocation strategy for distributed computing systems while minimizing the cost function including response time and service cost. First, based on the proposed cost function, we derive the optimal request scheduling policy and the optimal resource allocation policy synchronously. Second, considering the effects of incoming requests on the scheduling policy, the additive increase multiplicative decrease (AIMD) mechanism is implemented to model the relation between the request arrival and scheduling. In particular, the AIMD parameters can be designed such that the derived optimal strategy is still valid. Finally, a numerical example is presented to illustrate the derived results.

Traceless Genetic Programming (TGP) is a new Genetic Programming (GP) that may be used for solving difficult real-world problems. The main difference between TGP and other GP techniques is that TGP does not explicitly store the evolved computer programs. In this paper, TGP is used for solving real-world classification problems taken from PROBEN1. Numerical experiments show that TGP performs similar and sometimes even better than other GP techniques for the considered test problems.

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.