论文标题
无重格学习中的最后一次迭代收敛：凸孔concave景观的最低限值优化
Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes
论文作者
论文摘要
在最近的一系列论文中，已经确定了梯度下降/上升和镜像下降的变体在convex-concave零和游戏中表现出最后的迭代融合。具体而言，对于\ textit {不约束} min-max优化的情况，\ cite {disz17，liangs18}显示所谓的“乐观梯度下降/上升”的最后迭代收敛。此外，在\ cite {Metal}中，作者显示了带有额外渐变步骤的镜像下降显示了凸出问题的最后迭代收敛性（均未受到约束和不受约束），尽管他们的算法并未遵循在线学习框架；它使用额外的信息而不是\ textit {仅}记录来计算下一个迭代。在这项工作中，我们表明了“乐观的乘法更新（OMWU）”，该框架遵循No-Regret在线学习框架，在convex-concave游戏中展示了最后的互感，从而概括了\ cite {dp19}的结果{dp19}的结果，仅显示了Omwu的最后一个迭代的融合，仅显示了omwu的最后融合。我们通过指示该方法快速收敛的实验来补充结果。
In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate convergence of the so called "Optimistic Gradient Descent/Ascent" for the case of \textit{unconstrained} min-max optimization. Moreover, in \cite{Metal} the authors show that Mirror Descent with an extra gradient step displays last iterate convergence for convex-concave problems (both constrained and unconstrained), though their algorithm does not follow the online learning framework; it uses extra information rather than \textit{only} the history to compute the next iteration. In this work, we show that "Optimistic Multiplicative-Weights Update (OMWU)" which follows the no-regret online learning framework, exhibits last iterate convergence locally for convex-concave games, generalizing the results of \cite{DP19} where last iterate convergence of OMWU was shown only for the \textit{bilinear case}. We complement our results with experiments that indicate fast convergence of the method.
