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

Giuseppe Belgioioso; Sergio Grammatico

doi:10.1109/CDC.2018.8619610

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

Team Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

17 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018)
Editors	Andrew R. Teel, Magnus Egerstedt
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	3541-3546
ISBN (Electronic)	978-1538-1395-5
DOIs	https://doi.org/10.1109/CDC.2018.8619610
Publication status	Published - 2018
Event	CDC 2018: 57th IEEE Conference on Decision and Control - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Conference

Conference	CDC 2018: 57th IEEE Conference on Decision and Control
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

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10.1109/CDC.2018.8619610

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title = "A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games",

abstract = "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.",

author = "Giuseppe Belgioioso and Sergio Grammatico",

year = "2018",

doi = "10.1109/CDC.2018.8619610",

language = "English",

pages = "3541--3546",

editor = "Teel, {Andrew R. } and Egerstedt, {Magnus }",

booktitle = "Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018)",

publisher = "IEEE",

address = "United States",

note = "CDC 2018: 57th IEEE Conference on Decision and Control ; Conference date: 17-12-2018 Through 19-12-2018",

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Belgioioso, G & Grammatico, S 2018, A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games. in AR Teel & M Egerstedt (eds), Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018). IEEE, Piscataway, NJ, USA, pp. 3541-3546, CDC 2018: 57th IEEE Conference on Decision and Control, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8619610

A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games. / Belgioioso, Giuseppe; Grammatico, Sergio.
Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018). ed. / Andrew R. Teel; Magnus Egerstedt. Piscataway, NJ, USA: IEEE, 2018. p. 3541-3546.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AU - Grammatico, Sergio

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N2 - 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.

AB - 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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M3 - Conference contribution

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EP - 3546

BT - Proceedings of the 57th IEEE Conference on Decision and Control (CDC 2018)

A2 - Teel, Andrew R.

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T2 - CDC 2018: 57th IEEE Conference on Decision and Control

Y2 - 17 December 2018 through 19 December 2018

ER -

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

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