TY - GEN
T1 - Accelerated Gradient Play Algorithm for Distributed Nash Equilibrium Seeking
AU - Tatarenko, Tatiana
AU - Shi, Wei
AU - Nedich, Angelia
N1 - Funding Information:
*This work has been supported by the ONR grant no. N00014-12-1-0998.
Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - We study distributed algorithms for seeking a Nash equilibrium in a class of non-cooperative games with strongly monotone mappings. Each player has access to her own smooth local cost function and can communicate to her neighbors in some undirected graph. We first consider a distributed gradient play algorithm, which we call GRANE, for determining a Nash equilibrium. The algorithm involves every player performing a gradient step to minimize her own cost function while sharing and retrieving information locally among her neighbors in the network. We prove the convergence of this algorithm to a Nash equilibrium with a geometric rate. Further, we introduce the Nesterov type acceleration for the gradient play algorithm. We demonstrate that, similarly to the accelerated algorithms in centralized optimization and variational inequality problems, our accelerated algorithm outperforms GRANE in the convergence rate.
AB - We study distributed algorithms for seeking a Nash equilibrium in a class of non-cooperative games with strongly monotone mappings. Each player has access to her own smooth local cost function and can communicate to her neighbors in some undirected graph. We first consider a distributed gradient play algorithm, which we call GRANE, for determining a Nash equilibrium. The algorithm involves every player performing a gradient step to minimize her own cost function while sharing and retrieving information locally among her neighbors in the network. We prove the convergence of this algorithm to a Nash equilibrium with a geometric rate. Further, we introduce the Nesterov type acceleration for the gradient play algorithm. We demonstrate that, similarly to the accelerated algorithms in centralized optimization and variational inequality problems, our accelerated algorithm outperforms GRANE in the convergence rate.
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U2 - 10.1109/CDC.2018.8619479
DO - 10.1109/CDC.2018.8619479
M3 - Conference contribution
AN - SCOPUS:85062195662
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3561
EP - 3566
BT - 2018 IEEE Conference on Decision and Control, CDC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 57th IEEE Conference on Decision and Control, CDC 2018
Y2 - 17 December 2018 through 19 December 2018
ER -