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In this paper we consider a network scenario in which agents can evaluate each other according to a score graph that models some physical or social interaction. The goal is to design a distributed protocol, run by the agents, allowing them to learn their unknown state among a finite set of possible values. We propose a Bayesian framework in which scores and states are associated to probabilistic events with unknown parameters and hyperparameters respectively. We prove that each agent can learn its state by means of a local Bayesian classifier and a (centralized) Maximum-Likelihood (ML) estimator of the parameter-hyperparameter that combines plain ML and Empirical Bayes approaches. By using tools from graphical models, which allow us to gain insight on conditional dependences of scores and states, we provide two relaxed probabilistic models that ultimately lead to ML parameter-hyperparameter estimators amenable to distributed computation. In order to highlight the appropriateness of the proposed relaxations, we demonstrate the distributed estimators on a machine-to-machine testing set-up for anomaly detection and on a social interaction set-up for user profiling.

In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under asynchronous, unreliable and directed communication. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: (i) a verification in which they check---in a randomized fashion---the robust feasibility of a candidate optimal point, and (ii) an optimization step in which they exchange their candidate basis (the minimal set of constraints defining a solution) with neighbors and locally solve an optimization problem. As main result, we show that processors can stop the algorithm after a finite number of communication rounds (either because verification has been successful for a sufficient number of rounds or because a given threshold has been reached), so that candidate optimal solutions are consensual. The common solution is proven to be---with high confidence---feasible and hence optimal for the entire set of uncertainty except a subset having an arbitrary small probability measure. We show the effectiveness of the proposed distributed algorithm using two examples: a random, uncertain mixed-integer linear program and a distributed localization in wireless sensor networks. The distributed algorithm is implemented on a multi-core platform in which the nodes communicate asynchronously., Comment: Submitted for publication. arXiv admin note: text overlap with arXiv:1706.00488

In this paper, we consider a general challenging distributed optimization setup arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local variable, subject to local and coupling constraints, with the latter involving all the decision variables. We propose a novel fully distributed algorithm based on a relaxation of the primal problem and an elegant exploration of duality theory. Despite its complex derivation, based on several duality steps, the distributed algorithm has a very simple and intuitive structure. That is, each node finds a primal-dual optimal solution pair of a local relaxed version of the original problem and then updates suitable auxiliary local variables. We prove that agents asymptotically compute their portion of an optimal (feasible) solution of the original problem. This primal recovery property is obtained without any averaging mechanism typically used in dual decomposition methods. To corroborate the theoretical results, we show how the methodology applies to an instance of a distributed model-predictive control scheme in a microgrid control scenario.

This article deals with distributed control of microgrids composed of storages, generators, renewable energy sources, and critical and controllable loads. We consider a stochastic formulation of the optimal control problem associated with the microgrid that appropriately takes into account the unpredictable nature of the power generated by renewables. The resulting problem is a mixed-integer linear program and is NP-hard and nonconvex. Moreover, the peculiarity of the considered framework is that no central unit can be used to perform the optimization, but rather the units must cooperate with each other by means of neighboring communication. To solve the problem, we resort to a distributed methodology based on a primal decomposition approach. The resulting algorithm is able to compute high-quality feasible solutions to a two-stage stochastic optimization problem, for which we also provide a theoretical upper bound on the constraint violation. Finally, a Monte Carlo numerical computation on a scenario with a large number of devices shows the efficacy of the proposed distributed control approach. The numerical experiments are performed on realistic scenarios obtained from Generative Adversarial Networks (GANs) trained an open-source historical dataset of the EU.

From ancient times, the Mediterranean basin has connected peoples from different countries, facilitating both commercial and cultural exchanges. Within the Mediterranean basin, both large and small islands have always been transit and temporary stopping places, thereby promoting trade and acting as sorting centers for goods and knowledge. Today, these territories, which differ in size, population and economic and cultural activities, are the core of new exchanges and activities, among which tourism stands out. The Mediterranean basin has more than 100 islands belonging to six states that are members of the European Union (EU). However, despite the diversity and uniqueness of each island, these territories share the same permanent handicaps as a result of their insularity. This condition has been recognized by the EU as both a geo-cultural factor and a permanent handicap because of additional constraints on competitiveness in the areas concerned and is seen as the main reason for the formulation of specific policies addressed to these territories. Awareness of such a condition has developed recently, dating back to the end of the last century, and has led to the insular areas being identified as regions ‘which suffer from severe or permanent natural or demographic handicaps’ for which it is necessary to adopt specific measures aiming to ‘reduce disparities between the levels of development of the various regions and the backwardness of the least favored regions’. In contrast to these difficulties, Mediterranean islands experience a strong tourist demand that ensures high levels of tourism consumption with positive effects on local employment and production. Not only does tourism in islands tend to be central for the local economy, it is also the principal factor of economic, environmental and social imbalances. However, the islands cannot all be placed at the same stage of tourism development (Butler 1980), because in the Mediterranean destinations coexist at various stages of maturity. This makes it impossible to formulate strategic guidelines of sustainable development that are valid and generally applicable in all islands (Baldacchino, 2006; Fairbairn, 2007). It is, therefore, necessary to start from a comparative analysis of tourism in the islands to develop the most appropriate tourism policies for the territory concerned.

We consider a multi-agent setting with agents exchanging information over a possibly time-varying network, aiming at minimising a separable objective function subject to constraints. To achieve this objective we propose a novel subgradient averaging algorithm that allows for non-differentiable objective functions and different constraint sets per agent. Allowing different constraints per agent simultaneously with a time-varying communication network constitutes a distinctive feature of our approach, extending existing results on distributed subgradient methods. To highlight the necessity of dealing with a different constraint set within a distributed optimisation context, we analyse a problem instance where an existing algorithm does not exhibit a convergent behaviour if adapted to account for different constraint sets. For our proposed iterative scheme we show asymptotic convergence of the iterates to a minimum of the underlying optimisation problem for step sizes of the form η k + 1 , η > 0 . We also analyse this scheme under a step size choice of η k + 1 , η > 0 , and establish a convergence rate of O ( ln k k ) in objective value. To demonstrate the efficacy of the proposed method, we investigate a robust regression problem and an l 2 regression problem with regularisation .

In this paper we deal with a network of computing agents with local processing and neighboring communication capabilities that aim at solving (without any central unit) a submodular optimization problem. The cost function is the sum of many local submodular functions and each agent in the network has access to one function in the sum only. In this \emph{distributed} set-up, in order to preserve their own privacy, agents communicate with neighbors but do not share their local cost functions. We propose a distributed algorithm in which agents resort to the Lov\`{a}sz extension of their local submodular functions and perform local updates and communications in terms of single blocks of the entire optimization variable. Updates are performed by means of a greedy algorithm which is run only until the selected block is computed, thus resulting in a reduced computational burden. The proposed algorithm is shown to converge in expected value to the optimal cost of the problem, and an approximate solution to the submodular problem is retrieved by a thresholding operation. As an application, we consider a distributed image segmentation problem in which each agent has access only to a portion of the entire image. While agents cannot segment the entire image on their own, they correctly complete the task by cooperating through the proposed distributed algorithm.

Così come la Sicilia, nella metafora letteraria, anche le sue città sono plurali, possiedono identità molteplici. Palermo è il compendio di forme derivanti dai modi di abitare che nei secoli si sono succeduti, prodotte dalle popolazioni e da culture che hanno attraversato e modificato il contesto urbano, accogliendo e negando valori, intersecandosi, mescolandosi, dando origine a un sistema ricco di relazioni e denso di voci e di storia. Dobbiamo avere la consapevolezza di questi attraversamenti: migrazioni di uomini, di culture, di linguaggi e di forme dell’abitare. Ma questa grande ricchezza di manifestazioni necessita sempre di un continuo riconoscimento, di una comprensione autentica, scevra da pregiudizi, capace di associare a ogni immagine fisica le ragioni da cui essa è scaturita e a ogni linguaggio, lo spessore delle tradizioni che esso esprime e ci tramanda. Così si può restituire dignità e ricercare la bellezza che risiede in un principio, non più evidente, ma sempre vivo. La città, infatti, è molto più che la sua più che la sua dimensione fisica e spaziale, essa consiste soprattutto nell’immanenza del luogo, della sua identità e nei suoi significati stabili e indelebili. Just like Sicily, in the literary metaphor, its cities are also plural, they have multiple identities. Palermo is the compendium of forms deriving from the ways of living that have followed one another over the centuries, produced by the populations and cultures that have crossed and modified the urban context, welcoming and denying values, intersecting, mixing, giving rise to a system rich in relationships and full of voices and history. We must be aware of these crossings: migrations of men, cultures, languages ​​and forms of living. But this great wealth of manifestations always requires continuous recognition, an authentic understanding, free from prejudices, capable of associating the reasons from which it arose to each physical image and to each language, the depth of the traditions that it expresses and passes on to us. . Thus it is possible to restore dignity and seek the beauty that resides in a principle, no longer evident, but always alive. The city, in fact, is much more than its own rather than its physical and spatial dimension, it consists above all in the immanence of the place, its identity and its stable and indelible meanings.

In this paper we introduce disropt, a Python package for distributed optimization over networks. We focus on cooperative set-ups in which an optimization problem must be solved by peer-to-peer processors (without central coordinators) that have access only to partial knowledge of the entire problem. To reflect this, agents in disropt are modeled as entities that are initialized with their local knowledge of the problem. Agents then run local routines and communicate with each other to solve the global optimization problem. A simple syntax has been designed to allow for an easy modeling of the problems. The package comes with many distributed optimization algorithms that are already embedded. Moreover, the package provides full-fledged functionalities for communication and local computation, which can be used to design and implement new algorithms. disropt is available at github.com/disropt/disropt under the GPL license, with a complete documentation and many examples.

We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to have a composite structure and to consist of a known time-varying (engineering) part and an unknown (user-specific) part. Regarding the unknown part, it is assumed to have a known parametric (e.g., quadratic) structure a priori, whose parameters are to be learned along with the evolution of the algorithm. The algorithm is composed of two intertwined components: (i) a dynamic gradient tracking scheme for finding local solution estimates and (ii) a recursive least squares scheme for estimating the unknown parameters via user's noisy feedback on the local solution estimates. The algorithm is shown to exhibit a bounded regret under suitable assumptions. Finally, a numerical example corroborates the theoretical analysis.

In this paper, we consider a multi-objective optimization problem over networks in which agents aim to maximize their own objective function, while satisfying both local and coupling constraints. This set up includes, e.g., the computation of optimal steady states in multi-agent control systems. Since fairness is a key feature required for the solution, we resort to Cooperative Game Theory and search for the Nash bargaining solution among all the efficient (or Pareto optimal) points of a bargaining game. We propose a negotiation mechanism among the agents to compute such a solution in a distributed way. The problem is reformulated as the maximization of a properly weighted sum of the objective functions. The proposed algorithm is then a two step procedure in which local estimates of the Nash bargaining weights are updated online and existing distributed optimization algorithms are applied. The proposed method is formally analyzed for a particular case, while numerical simulations are provided to corroborate the theoretical findings and to demonstrate its efficacy

The new perspective for planning wants to build a broad framework of studies, research on the challenges that the cities of the world must face today in order to find new conditions of balance between the need for economic development and the limits of environmental carrying capacity. Until a few decades ago, attention to the environment stopped at verifying the impacts of anthropogenic activities on the territories and city life was one of the causes of these environmental impacts. Today, ecosystem sustainability policies have become the starting point for all development policies equipped with scientific analysis and reliability. Of course, this change has not occurred all over the planet and, as everyone knows, some important national governments no longer intend to recognize the fact that some of the human productive activities are capable of destroying not only the life of cities but of the whole planet.

Editors: Karina von Schuckmann; Pierre-Yves Le Traon.-- Review Editors: Neville Smith (Chair); Ananda Pascual; Samuel Djavidnia; Jean-Pierre Gattuso; Marilaure Grégoire; Glenn Nolan., The authors would like to thank the Institut Cartogràfic i Geològic de Catalunya (ICGC) for providing data. Thanks are due to FCT/MCTES for the financial support to CESAM (UID/AMB/50017/2019), through national funds., Chapter 1: Introduction and the European Environment policy framework.-- CMEMS OSR4, Chapter 2: State, variability and change in the ocean.-- CMEMS OSR4, Chapter 3: Case studies.-- CMEMS OSR4, Chapter 4: Specific events 2018.

We consider a multi-agent setting with agents exchanging information over a network to solve a convex constrained optimisation problem in a distributed manner. We analyse a new algorithm based on local subgradient exchange under undirected time-varying communication. First, we prove asymptotic convergence of the iterates to a minimum of the given optimisation problem for time-varying step-sizes of the form $c(k) = \frac{\eta }{{k + 1}}$, for some η > 0. We then restrict attention to step-size choices $c(k) = \frac{\eta }{{\sqrt {k + 1} }},\eta > 0$, and establish a convergence of $\mathcal{O}\left( {\frac{{\ln (k)}}{{\sqrt k }}} \right)$ in objective value. Our algorithm extends currently available distributed subgradient/proximal methods by: (i) accounting for different constraint sets at each node, and (ii) enhancing the convergence speed thanks to a subgradient averaging step performed by the agents. A numerical example demonstrates the efficacy of the proposed algorithm.

In this paper we deal with distributed optimal control for nonlinear dynamical systems over graph, that is large-scale systems in which the dynamics of each subsystem depends on neighboring states only. Starting from a previous work in which we designed a partially distributed solution based on a cloud, here we propose a fully-distributed algorithm. The key novelty of the approach in this paper is the design of a sparse controller to stabilize trajectories of the nonlinear system at each iteration of the distributed algorithm. The proposed controller is based on the design of a stabilizing controller for polytopic Linear Parameter Varying (LPV) systems satisfying nonconvex sparsity constraints. Thanks to a suitable choice of vertex matrices and to an iterative procedure using convex approximations of the nonconvex matrix problem, we are able to design a controller in which each agent can locally compute the feedback gains at each iteration by simply combining coefficients of some vertex matrices that can be pre-computed offline. We show the effectiveness of the strategy on simulations performed on a multi-agent formation control problem.

We consider a network scenario in which agents can evaluate each other according to a score graph that models some interactions. The goal is to design a distributed protocol, run by the agents, that allows them to learn their unknown state among a finite set of possible values. We propose a Bayesian framework in which scores and states are associated to probabilistic events with unknown parameters and hyperparameters, respectively. We show that each agent can learn its state by means of a local Bayesian classifier and a (centralized) Maximum-Likelihood (ML) estimator of parameter-hyperparameter that combines plain ML and Empirical Bayes approaches. By using tools from graphical models, which allow us to gain insight on conditional dependencies of scores and states, we provide a relaxed probabilistic model that ultimately leads to a parameter-hyperparameter estimator amenable to distributed computation. To highlight the appropriateness of the proposed relaxation, we demonstrate the distributed estimators on a social interaction set-up for user profiling., This submission is a shorter work (for conference publication) of a more comprehensive paper, already submitted as arXiv:1706.04081 (under review for journal publication). In this short submission only one social set-up is considered and only one of the relaxed estimators is proposed. Moreover, the exhaustive analysis, carried out in the longer manuscript, is completely missing in this version