Single-Timescale Distributed GNE Seeking for Aggregative Games Over Networks via Forward–Backward Operator Splitting

Gadjov, Dian; Pavel, Lacra

doi:10.1109/tac.2020.3015354

Cited by 51 publications

(50 citation statements)

References 26 publications

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“…A variety of NE seeking algorithms, for the partial-decision information setting, have been proposed, e.g. [10]- [11]. However, all these results require strict/strong monotonicity of the pseudo-gradient.…”

Section: Introductionmentioning

confidence: 99%

On the exact convergence to Nash equilibrium in monotone regimes under partial-information

Gadjov

Pavel

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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In this paper, we consider distributed Nash equilibrium seeking in monotone and hypomonotone games. We first assume that each player has knowledge of the opponents' decisions and propose a passivity-based modification of the standard gradient-play dynamics, that we call "Heavy Anchor". We prove that Heavy Anchor allows a relaxation of strict monotonicity of the pseudo-gradient, needed for gradient-play dynamics, and can ensure exact asymptotic convergence in merely monotone regimes. We extend these results to the setting where each player has only partial information of the opponents' decisions. Each player maintains a local decision variable and an auxiliary state estimate, and communicates with their neighbours to learn the opponents' actions. We modify Heavy Anchor via a distributed Laplacian feedback and show how we can exploit equilibrium-independent passivity properties to achieve convergence to a Nash equilibrium in hypomonotone regimes. N j=1 w ij . Assume that W = W T so the weighted Laplacian of G is L = Deg − W . When G is connected and undirected, 0 is a simple eigenvalue of L, L1 N = 0, 1 T N L = 0 T , and all other eigenvalues are positive, 0 < λ 2 (L) ≤ • • • ≤ λ N (L).

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Section: Introductionmentioning

confidence: 99%

On the exact convergence to Nash equilibrium in monotone regimes under partial-information

Gadjov

Pavel

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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“…Usually, A : R n ⇒ R n and B : R n → R n are a set valued and a single valued monotone operator, respectively. Inclusions as the above arise systematically in convex optimization [5,19,35,90] and generalized Nash equilibrium problems in convex-monotone games [11,14,21,107,108,109].…”

Section: Applications Of Convergent Deterministic Sequencesmentioning

confidence: 99%

Convergence of sequences: a survey

Franci¹,

Grammatico²

2021

Preprint

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Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an overview of the literature on convergence theorems and their connection with Féjer monotonicity in the deterministic and stochastic settings, and we show how to exploit these results.

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“…The authors of [18] design a continuous-time algorithm based on the projected dynamics and non-smooth tracking strategy, which is only applicable if the coupling constraints can be expressed as a system of linear equations. More recently, [19], [20] introduce local estimates of the aggregates of interest, and then leverage the forwardbackward splitting and proximal-point algorithms to compute the GNEs, respectively. The authors of [21] further develop an algorithm that can deal with time-varying communication networks by integrating the projected pseudo-gradient scheme with dynamic tracking.…”

Section: Imentioning

confidence: 99%

“…Here, 𝜆 𝑖 is the Lagrange multiplier enforcing the resource constraints 𝐴 𝑖 𝑥 𝑖 + 𝜎 𝑖 ≤ 𝑐; 𝑑 𝑖 is the multiplier enforcing the correct aggregate estimation, i.e., 𝜎 𝑖 = 𝑗 ∈N −𝑖 𝐴 𝑗 𝑥 𝑗 . Notably, besides the explicit local problem formulation of agent 𝑖 in (4), the decision vector 𝑥 𝑖 is also involved in the constraints 𝜎 𝑗 = 𝑝 ∈N − 𝑗 𝐴 𝑝 𝑥 𝑝 for all 𝑗 ∈ N −𝑖 , and that is why we need to incorporate 𝑗 ∈N −𝑖 (−𝐴 𝑇 𝑖 𝑑 𝑗 ) into the first inclusion of(19).We assume that for each agent 𝑖 ∈ N , its local optimization problem(4) admits a minimizer 𝑥 * 𝑖 . Let 𝑥 * [𝑥 * 𝑖 ] 𝑖 ∈N .…”

mentioning

confidence: 99%

A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks

Huang¹,

Hu²

2021

Preprint

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We consider a class of multi-agent optimization problems, where each agent has a local objective function that depends on its own decision variables and the aggregate of others, and is willing to cooperate with other agents to minimize the sum of the local objectives. After associating each agent with an auxiliary variable and the related local estimates, we conduct primal decomposition to the globally coupled problem and reformulate it so that it can be solved distributedly. Based on the Douglas-Rachford method, an algorithm is proposed which ensures the exact convergence to a solution of the original problem. The proposed method enjoys desirable scalability by only requiring each agent to keep local estimates whose number grows linearly with the number of its neighbors. We illustrate our proposed algorithm by numerical simulations on a commodity distribution problem over a transport network.

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Single-Timescale Distributed GNE Seeking for Aggregative Games Over Networks via Forward–Backward Operator Splitting

Cited by 51 publications

References 26 publications

On the exact convergence to Nash equilibrium in monotone regimes under partial-information

On the exact convergence to Nash equilibrium in monotone regimes under partial-information

Convergence of sequences: a survey

A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks

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