The distributed computation of equilibria and optima has seen growing interest in a broad collection of networked problems. We consider the computation of equilibria of convex stochastic Nash games characterized by a possibly nonconvex potential function. Our focus is on two classes of stochastic Nash games: (P1): A potential stochastic Nash game, in which each player solves a parameterized stochastic convex program; and (P2): A misspecified generalization, where the player-specific stochastic program is complicated by a parametric misspecification. In both settings, exact proximal BR solutions are generally unavailable in finite time since they necessitate solving parameterized stochastic programs. Consequently, we design two asynchronous inexact proximal BR schemes to solve the problems, where in each iteration a single player is randomly chosen to compute an inexact proximal BR solution with rivals' possibly outdated information. Yet, in the misspecified regime (P2), each player possesses an extra estimate of the misspecified parameter and updates its estimate by a projected stochastic gradient (SG) algorithm. By Since any stationary point of the potential function is a Nash equilibrium of the associated game, we believe this paper is amongst the first ones for stochastic nonconvex (but block convex) optimization problems equipped with almost-sure convergence guarantees. These statements can be extended to allow for accommodating weighted potential games and generalized potential games. Finally, we present preliminary numerics based on applying the proposed schemes to congestion control and Nash-Cournot games.

中文翻译：

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随机和错误指定的潜在博弈的异步方案和非凸优化

平衡和最优的分布式计算已引起人们对广泛的网络问题的浓厚兴趣。我们考虑以可能为非凸势函数为特征的凸型随机Nash博弈均衡的计算。我们的重点是两类随机Nash游戏：（P1）：一种潜在的随机Nash游戏，其中每个玩家都解决一个参数化的随机凸程序。（P2）：一个错误指定的概括，其中特定于玩家的随机程序由于参数错误指定而变得复杂。在这两种情况下，由于需要求解参数化的随机程序，因此在有限的时间内通常无法获得精确的近端BR解。因此，我们设计了两种异步不精确的近端BR方案来解决这些问题，其中，在每次迭代中，随机选择一个玩家来计算竞争对手可能过时的信息的不精确的近端BR解决方案。然而，在错误指定的状态（P2）中，每个玩家都对错误指定的参数拥有额外的估计，并通过投影随机梯度（SG）算法更新其估计。由于潜在函数的任何平稳点都是相关博弈的Nash均衡，因此我们认为本文是针对随机非凸（但块凸）优化问题的第一部分，该问题具有几乎确定的收敛性保证。这些陈述可以扩展以允许容纳加权潜在游戏和广义潜在游戏。最后，在提出的方案应用于拥塞控制和Nash-Cournot游戏的基础上，我们提出了初步的数值。