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Sergio Grammatico

Publications and source records attributed to Sergio Grammatico.

At least 91 records · Page 5Linked to original sources
arXiv2020

Distributed Forward-Backward algorithms for stochastic generalized Nash equilibrium seeking

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEP, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. As main contribution, we show almost sure convergence of our proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive. For non-generalized SNEPs, we show almost sure convergence also if the pseudogradient mapping is restricted strictly monotone. Numerical simulations show that the proposed forward-backward algorithm seems faster that other available algorithms.

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arXiv2020

A damped forward-backward algorithm for stochastic generalized Nash equilibrium seeking

We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward-backward operator splitting and a suitable preconditioning matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo-gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.

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arXiv2020

Distributed forward-backward (half) forward algorithms for generalized Nash equilibrium seeking

We present two distributed algorithms for the computation of a generalized Nash equilibrium in monotone games. The first algorithm follows from a forward-backward-forward operator splitting, while the second, which requires the pseudo-gradient mapping of the game to be cocoercive, follows from the forward-backward-half-forward operator splitting. Finally, we compare them with the distributed, preconditioned, forward-backward algorithm via numerical experiments.

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arXiv2020

Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks

We design the first fully-distributed algorithm for generalized Nash equilibrium seeking in aggregative games on a time-varying communication network, under partial-decision information, i.e., the agents have no direct access to the aggregate decision. The algorithm is derived by integrating dynamic tracking into a projected pseudo-gradient algorithm. The convergence analysis relies on the framework of monotone operator splitting and the Krasnosel'skii-Mann fixed-point iteration with errors.

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arXiv2019

Distributed payoff allocation in coalitional games via time varying paracontractions

We present a partial operator-theoretic characterization of approachability principle and based on this characterization, we interpret a particular distributed payoff allocation algorithm to be a sequence of time-varying paracontractions. Further, we also propose a distributed algorithm, under the context of coalitional game, on time-varying communication networks. The state in the proposed algorithm converges to a consensus within, the predefined, desired set. For convergence analysis, we rely on the operator-theoretic property of paracontraction.

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arXiv2019

An integral Nash equilibrium control scheme for a class of multi-agent linear systems

We propose an integral Nash equilibrium seeking control (I-NESC) law which steers the multi-agent system composed of a special class of linear agents to the neighborhood of the Nash equilibrium in noncooperative strongly monotone games. First, we prove that there exist parameters of the integral controller such that the system converges to the Nash equilibrium in the full-information case, in other words, without the parameter estimation scheme used in extremum seeking algorithms. Then we prove that there exist parameters of the I-NESC such that the system converges to the neighborhood of the Nash equilibrium in the limited information case where parameter estimation is used. We provide a simulation example that demonstrates that smaller perturbation frequencies and amplitudes are needed to attain similar convergence speed as the existing state-of-the-art algorithm.

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arXiv2019

Time-varying constrained proximal type dynamics in multi-agent network games

In this paper, we study multi-agent network games subject to affine time-varying coupling constraints and a time-varying communication network. We focus on the class of games adopting proximal dynamics and study their convergence to a persistent equilibrium. The assumptions considered to solve the problem are discussed and motivated. We develop an iterative equilibrium seeking algorithm, using only local information, that converges to a special class of game equilibria. Its derivation is motivated by several examples, showing that the original game dynamics fail to converge. Finally, we apply the designed algorithm to solve a constrained consensus problem, validating the theoretical results.

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arXiv2019

A preconditioned Forward-Backward method for partially separable SemiDefinite Programs

We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semidefinite programs (SDPs). We exploit a chordal aggregate sparsity pattern assumption on the original SDP to obtain a set of mutually coupled SDPs defined on positive semidefinite (PSD) cones of reduced dimensions. We show that the proposed algorithms converge to a solution of the original SDP via iterations of reasonable computational cost. Finally, we compare the performances of the two proposed algorithms with respect to others available in the literature.

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arXiv2019

Charging plug-in electric vehicles as a mixed-integer aggregative game

We consider the charge scheduling coordination of a fleet of plug-in electric vehicles, developing a hybrid decision-making framework for efficient and profitable usage of the distribution grid. Each charging dynamics, affected by the aggregate behavior of the whole fleet, is modelled as an inter-dependent, mixed-logical-dynamical system. The coordination problem is formalized as a generalized mixed-integer aggregative potential game, and solved via semi-decentralized implementation of a sequential best-response algorithm that leads to an approximated equilibrium of the game.

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arXiv2019

Convergence in uncertain linear systems

State convergence is essential in several scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, monotone game theory, multi-agent learning over time-varying networks. This paper is the first on state convergence in both continuous- and discrete-time linear systems affected by polytopic uncertainty. First, we characterize state convergence in linear time invariant systems via equivalent necessary and sufficient conditions. In the presence of uncertainty, we complement the canonical definition of (weak) convergence with a stronger notion of convergence, which requires the existence of a common kernel among the generator matrices of the difference/differential inclusion (strong convergence). We investigate under which conditions the two definitions are equivalent. Then, we characterize weak and strong convergence by means of Lyapunov and LaSalle arguments, (linear) matrix inequalities and separability of the eigenvalues of the generator matrices. We also show that, unlike asymptotic stability, state convergence lacks of duality.

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arXiv2019

Asynchronous and time-varying proximal type dynamics multi-agent network games

In this paper, we study proximal type dynamics in the context of noncooperative multi-agent network games. These dynamics arise in different applications, since they describe distributed decision making in multi-agent networks, e.g., in opinion dynamics, distributed model fitting and network information fusion, where the goal of each agent is to seek an equilibrium using local information only. We analyse several conjugations of this class of games, providing convergence results, or designing equilibrium seeking algorithms when the original dynamics fail to converge. For the games subject only to local constraints we look into both synchronous/asynchronous dynamics and time-varying communication networks. For games subject in addition to coupling constraints, we design an equilibrium seeking algorithm converging to a special class of game equilibria. Finally, we validate the theoretical results via numerical simulations on opinion dynamics and distributed model fitting.

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arXiv2019

An asynchronous, forward-backward, distributed generalized Nash equilibrium seeking algorithm

In this paper, we propose an asynchronous distributed algorithm for the computation of generalized Nash equilibria in noncooperative games, where the players interact via an undirected communication graph. Specifically, we extend the paper "Asynchronous distributed algorithm for seeking generalized Nash equilibria" by Yi and Pavel: we redesign the asynchronous update rule using auxiliary variables over the nodes rather than over the edges. This key modification renders the algorithm scalable for highly interconnected games. The derived asynchronous algorithm is robust against delays in the communication and it eliminates the idle times between computations, hence modeling a more realistic interaction between players with different update frequencies. We address the problem from an operator-theoretic perspective and design the algorithm via a preconditioned forward-backward splitting. Finally, we numerically simulate the algorithm for the Cournot competition in networked markets.

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arXiv2018

Distributed averaging integral Nash equilibrium seeking on networks

Continuous-time gradient-based Nash equilibrium seeking algorithms enjoy a passivity property under a suitable monotonicity assumption. This feature has been exploited to design distributed algorithms that converge to Nash equilibria and use local information only. We further exploit the passivity property to interconnect the algorithms with distributed averaging integral controllers that tune on-line the weights of the communication graph. The main advantage is to guarantee convergence to a Nash equilibrium without requiring a strong coupling condition on the algebraic connectivity of the communication graph over which the players exchange information, nor a global high-gain.

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arXiv2018

Towards time-varying proximal dynamics in Multi-Agent Network Games

Distributed decision making in multi-agent networks has recently attracted significant research attention thanks to its wide applicability, e.g. in the management and optimization of computer networks, power systems, robotic teams, sensor networks and consumer markets. Distributed decision-making problems can be modeled as inter-dependent optimization problems, i.e., multi-agent game-equilibrium seeking problems, where noncooperative agents seek an equilibrium by communicating over a network. To achieve a network equilibrium, the agents may decide to update their decision variables via proximal dynamics, driven by the decision variables of the neighboring agents. In this paper, we provide an operator-theoretic characterization of convergence with a time-invariant communication network. For the time-varying case, we consider adjacency matrices that may switch subject to a dwell time. We illustrate our investigations using a distributed robotic exploration example.

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arXiv2018

A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games

We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.

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arXiv2018

Projected-gradient algorithms for generalized equilibrium seeking in Aggregative Games are preconditioned Forward-Backward methods

We show that projected-gradient methods for the distributed computation of generalized Nash equilibria in aggregative games are preconditioned forward-backward splitting methods applied to the KKT operator of the game. Specifically, we adopt the preconditioned forward-backward design, recently conceived by Yi and Pavel in the manuscript "A distributed primal-dual algorithm for computation of generalized Nash equilibria via operator splitting methods" for generalized Nash equilibrium seeking in aggregative games. Consequently, we notice that two projected-gradient methods recently proposed in the literature are preconditioned forward-backward methods. More generally, we provide a unifying operator-theoretic ground to design projected-gradient methods for generalized equilibrium seeking in aggregative games.

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arXiv2018

Continuous-time integral dynamics for Aggregative Game equilibrium seeking

In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results.

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