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This work studies Nash equilibrium seeking for a class of stochasticaggregative games, where each player has an expectation-valued objectivefunction depending on its local strategy and the aggregate of all players'strategies. We propose a distributed algorithm with operator extrapolation, inwhich each player maintains an estimate of this aggregate by exchanging thisinformation with its neighbors over a time-varying network, and updates itsdecision through the mirror descent method. An operator extrapolation at thesearch direction is applied such that the two step historical gradient samplesare utilized to accelerate the convergence. Under the strongly monotoneassumption on the pseudo-gradient mapping, we prove that the proposed algorithmcan achieve the optimal convergence rate of $\mathcal{O}(1/k)$ for Nashequilibrium seeking of stochastic games. Finally, the algorithm performance isdemonstrated via numerical simulations.

An Optimal Distributed Algorithm with Operator Extrapolation for Stochastic Aggregative Games