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

Franci, Barbara; Staudigl, Mathias; Grammatico, Sergio

doi:10.23919/ecc51009.2020.9143676

Cited by 25 publications

(28 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[7], [8], [13]. However, these methods typically require more complex computations, such as the forward-backward-forward algorithm, [14] [8], Tikhonov proximal-point algorithm in [12], inexact proximal best-response in [5], [15], or proximal-point/resolvent computation (e.g. Douglas-Rachford splitting), [8].…”

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)

View full text Add to dashboard Cite

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).

show abstract

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)

View full text Add to dashboard Cite

show abstract

“…However, these properties are not necessarily enough to ensure convergence, hence, (quasi) Féjer monotonicity is often used in combination with convergence results on sequences of real numbers. These technical results have been used in many theoretical and computational applications that range from stochastic Nash equilibrium seeking [11,12,14] to machine learning [17,19,20].…”

Section: Lyapunov Decrease and Féjer Monotonicitymentioning

confidence: 99%

“…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%

“…The aim of this paper is to collect these results towards a complete overview, thus to be able to find the one that most suits the application at hand. In fact, many convergence results find their use in theoretical applications, such as Lyapunov stability analysis [1,2,3,4], variational analysis [5,6,7,8,9,10] and game equilibrium seeking [11,12,13,14], in automatic control, such as model predictive control [15] and network control problems [16], as well as in other engineering areas, e.g., training and learning in generative adversarial networks [17,18,19], vehicle flow control in traffic networks [20] and in modeling the prosumer behavior in smart power grids [11,14,21,22].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Convergence of sequences: a survey

Franci¹,

Grammatico²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Despite the advances in stochastic optimization and variational inequalities, the algorithmic treatment of general monotone inclusion problems under stochastic uncertainty is a largely unexplored field. This is rather surprising given the vast amount of applications of maximally monotone inclusions in control and engineering, encompassing distributed computation of generalized Nash equilibria [17,31,86], traffic systems [34,35,43], and PDE-constrained optimization [10]. The first major aim of this manuscript is to introduce and investigate a relaxed inertial stochastic forwardbackward-forward (RISFBF) method, building on an operator splitting scheme originally due to Paul Tseng [85].…”

Section: Contributionsmentioning

confidence: 99%

Stochastic Relaxed Inertial Forward-Backward-Forward splitting for Monotone Inclusions in Hilbert spaces

Cui,

Shanbhag,

Staudigl

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider monotone inclusions defined on a Hilbert space where the operator is given by the sum of a maximal monotone operator T and a single-valued monotone, Lipschitz continuous, and expectation-valued operator V. We draw motivation from the seminal work by Attouch and Cabot [1, 2] on relaxed inertial methods for monotone inclusions and present a stochastic extension of the relaxed inertial forward-backward-forward (RISFBF) method. Facilitated by an online variance reduction strategy via a mini-batch approach, we show that (RISFBF) produces a sequence that weakly converges to the solution set. Moreover, it is possible to estimate the rate at which the discrete velocity of the stochastic process vanishes. Under strong monotonicity, we demonstrate strong convergence, and give a detailed assessment of the iteration and oracle complexity of the scheme. When the mini-batch is raised at a geometric (polynomial) rate, the rate statement can be strengthened to a linear (suitable polynomial) rate while the oracle complexity of computing an -solution improves to O(1/ ). Importantly, the latter claim allows for possibly biased oracles, a key theoretical advancement allowing for far broader applicability. By defining a restricted gap function based on the Fitzpatrick function, we prove that the expected gap of an averaged sequence diminishes at a sublinear rate of O(1/k) while the oracle complexity of computing a suitably defined -solution is O(1/ 1+a ) where a > 1. Numerical results on two-stage games and an overlapping group Lasso problem illustrate the advantages of our method compared to stochastic forward-backward-forward (SFBF) and SA schemes.

show abstract

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

Cited by 25 publications

References 12 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

Stochastic Relaxed Inertial Forward-Backward-Forward splitting for Monotone Inclusions in Hilbert spaces

Contact Info

Product

Resources

About