论文标题
竞争性梯度优化
Competitive Gradient Optimization
论文作者
论文摘要
我们研究了零和游戏中固定点的收敛问题。我们提出了竞争性梯度优化（CGO），这是一种基于梯度的方法，它结合了零和游戏中两个玩家之间的交互以进行优化更新。我们提供了CGO及其收敛性能的连续时间分析，同时表明在连续极限中，CGO前辈退化为其梯度下降（GDA）变体。我们为固定点提供了收敛速度，并进一步提出了一类普遍的$α$ coherent函数，我们为此提供了收敛分析。我们表明，对于严格的$α$ coherent函数，我们的算法收敛到鞍点。此外，我们提出了一种乐观的CGO（OCGO），这是一种乐观的变体，为此，我们显示了与$α$ coherent函数类别的鞍点的收敛速率。
We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO ), a gradient-based method that incorporates the interactions between the two players in zero-sum games for optimization updates. We provide continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, CGO predecessors degenerate to their gradient descent ascent (GDA) variants. We provide a rate of convergence to stationary points and further propose a generalized class of $α$-coherent function for which we provide convergence analysis. We show that for strictly $α$-coherent functions, our algorithm convergences to a saddle point. Moreover, we propose optimistic CGO (OCGO), an optimistic variant, for which we show convergence rate to saddle points in $α$-coherent class of functions.
