Geodesic
Distributed accelerated Nash equilibrium learning for two-subnetwork zero-sum game with bilinear coupling
Kybernetika, Tome 59 (2023) no. 3, pp. 418-436.

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This paper proposes a distributed accelerated first-order continuous-time algorithm for $O({1}/{t^2})$ convergence to Nash equilibria in a class of two-subnetwork zero-sum games with bilinear couplings. First-order methods, which only use subgradients of functions, are frequently used in distributed/parallel algorithms for solving large-scale and big-data problems due to their simple structures. However, in the worst cases, first-order methods for two-subnetwork zero-sum games often have an asymptotic or $O(1/t)$ convergence. In contrast to existing time-invariant first-order methods, this paper designs a distributed accelerated algorithm by combining saddle-point dynamics and time-varying derivative feedback techniques. If the parameters of the proposed algorithm are suitable, the algorithm owns $O(1/t^2)$ convergence in terms of the duality gap function without any uniform or strong convexity requirement. Numerical simulations show the efficacy of the algorithm.
DOI : 10.14736/kyb-2023-3-0418
Classification : 37N40, 91A10, 93A14
Keywords: two-subnetwork zero-sum game; distributed accelerated algorithm; Nash equilibrium learning; nonsmooth function; continuous-time algorithm 
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     title = {Distributed accelerated {Nash} equilibrium learning for two-subnetwork zero-sum game with bilinear coupling},
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     pages = {418--436},
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Zeng, Xianlin; Dou, Lihua; Cui, Jinqiang. Distributed accelerated Nash equilibrium learning for two-subnetwork zero-sum game with bilinear coupling. Kybernetika, Tome 59 (2023) no. 3, pp. 418-436. doi : 10.14736/kyb-2023-3-0418. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2023-3-0418/

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