An Efficient Distributed Nash Equilibrium Seeking with Compressed and Event-triggered Communication.
CoRR(2023)
摘要
Distributed Nash equilibrium (NE) seeking problems for networked games have
been widely investigated in recent years. Despite the increasing attention,
communication expenditure is becoming a major bottleneck for scaling up
distributed approaches within limited communication bandwidth between agents.
To reduce communication cost, an efficient distributed NE seeking (ETC-DNES)
algorithm is proposed to obtain an NE for games over directed graphs, where the
communication efficiency is improved by event-triggered exchanges of compressed
information among neighbors. ETC-DNES saves communication costs in both
transmitted bits and rounds of communication. Furthermore, our method only
requires the row-stochastic property of the adjacency graph, unlike previous
approaches that hinged on double-stochastic communication matrices. We provide
convergence guarantees for ETC-DNES on games with restricted strongly monotone
mappings, testifying that such a communication method is efficient without
sacrificing the accuracy of the algorithm. The algorithm and analysis are
extended to a compressed algorithm with stochastic event-triggered mechanism
(SETC-DNES). In SETC-DNES, we introduce a random variable in the triggering
condition to further enhance algorithm efficiency. We demonstrate that
SETC-DNES guarantees linear convergence to the optimal NE while achieving even
greater reductions in communication costs compared to ETC-DNES. Finally,
numerical simulations illustrate the effectiveness of the proposed algorithms.
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