Nash equilibrium seeking under partial-decision information: Monotonicity, smoothness and proximal-point algorithms

Bianchi, Mattia; Grammatico, Sergio

doi:10.1109/cdc51059.2022.9993145

Cited by 1 publication

(5 citation statements)

References 20 publications

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“…Thus, Assumption 4 holds. We run Algorithm 1, where α i,k = (k + λ i ) −a and η i,k = (k + δ i ) −b with a = 0.8, b = 0.05, and each λ i and δ i are generated from the uniform distributions [4,5] and [2,3], respectively. Thus, Assumption 6 holds by recalling Remark 1.…”

Section: Numerical Studiesmentioning

confidence: 99%

“…Furthermore, [18] proposed a preconditioned forward-backward (PFB) method with variance reduction for the stochastic generalized Nash equilibrium problem, and proved its almost sure convergence to the variational GNE when the pseudogradient mapping is restricted monotone and cocoercive. Finally, [5] recently proposed a distributed preconditioned proximal-point (PPP) algorithm and provided convergence guarantees to a Nash equilibrium for restricted monotone but non-Lipschitz mapping.…”

Section: Prior Work On Ne Computationmentioning

confidence: 99%

“…In addition, [10,18,43] required that each player updates its strategy with its rival strategies while updating the dual variables based on the consensus protocol. Though [5] designed a fully distributed algorithm, it requires each player keep an estimate of all other players' strategies, which however is not communication-efficient. Our previous conference version [31] considered a special class of aggregative games in the deterministic regime and designed a Tikhonov regularization-bsed distributed computation method, where each player merely need to estimate aggregate and exchanges its aggregate estimate with neighbors over a communication network.…”

Section: Prior Work On Ne Computationmentioning

confidence: 99%

“…Let the production cost of firm i be c i (g i ; ξ i ) = ci +(κ i +ξ i ) T g i for κ i > 0, ci > 0 with ξ i being a mean-zero random variable. For each i ∈ N , let ci , each component of κ i and cap i be generated from the uniform distributions [5,6], [0.5, 0.6], and [2, 2.5], respectively. For each market l = 1, • • • , m, let d l and b l be generated from the uniform distributions [20,25] and [1, 1.5], respectively.…”

Section: Numerical Studiesmentioning

confidence: 99%

“…= ti g i with li and ti randomly generated from the uniform distribution [0, 1]. We run Algorithm 2 with α i,k = (k + λ i ) −0.75 , η i,k = (k + δ i ) −0.24 , and µ k = (k + 1) −0.24 , where λ i and δ i generated from the uniform distributions [4,5] and [2,3], respectively. Recall from Lemma 6 that x * is a Nash equilibrium to the private hierarchical game (48) if and only if there exists g * ∈ N i=1…”

Section: Extensions To Private Hierarchical Aggregative Gamesmentioning

confidence: 99%

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Distributed Computation of Nash Equilibria for Monotone Aggregative Games via Iterative Regularization

Lei

Shanbhag

Chen

2020

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

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We consider a class of N -player nonsmooth aggregative games over networks in stochastic regimes, where the ith player is characterized by a composite cost function f i +d i +r i , f i is a smooth expectationvalued function dependent on its own strategy and an aggregate function of rival strategies, d i is a convex hierarchical term dependent on its strategy, and r i is a nonsmooth convex function of its strategy with an efficient prox-evaluation. Though the aggregate is unknown to any given player, each player can interact with its neighbors to construct an estimate of the aggregate. We design a fully distributed iterative proximal stochastic gradient method overlaid by a Tikhonov regularization, where each player may independently choose its steplengths and regularization parameters while meeting some coordination requirements. Under a monotonicity assumption on the concatenated player-specific gradient mapping, we prove that the generated sequence converges almost surely to the least-norm Nash equilibrium (i.e., a Nash equilibrium with the smallest two-norm). In addition, for the case with each r i being an indicator function of a compact convex set, we establish the convergence rate associated with the expected gap function at the time-averaged sequence. Furthermore, we consider the extension to the private hierarchical regime where each player is a leader with respect to a collection of private followers competing in a strongly monotone game, parametrized by leader decisions. By leveraging a convolutionsmoothing framework, we present amongst the first fully distributed schemes for computing a Nash equilibrium of a game complicated by such a hierarchical structure. Based on this framework, we extend the rate statements to accommodate the computation of a hierarchical stochastic Nash equilibrium by using a Fitzpatrick gap function. Notably, both sets of fully distributed schemes display near-optimal sample-complexities, suggesting that this hierarchical structure does not lead to performance degradation. Finally, we validate the proposed methods on a networked Nash-Cournot equilibrium problem and a hierarchical generalization.

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Section: Numerical Studiesmentioning

confidence: 99%

Section: Prior Work On Ne Computationmentioning

confidence: 99%