论文标题
最后的迭代比平滑的凸孔鞍点问题平均迭代速度慢。
Last Iterate is Slower than Averaged Iterate in Smooth Convex-Concave Saddle Point Problems
论文作者
论文摘要
在本文中，我们研究了平滑的凸孔座鞍点问题。具体而言，我们分析了外部（例如）算法的最后迭代收敛属性。众所周知，例如$ O（1/t）$（Nemirovski，2004年）的Eg汇总（平均）迭代。在本文中，我们表明，EG的最后一个迭代以$ O（1/\ sqrt {t}）$的速率收敛。据我们所知，这是第一篇为平滑凸孔concave鞍点问题提供最后一次迭代的收敛速率保证的论文。此外，我们通过证明最后迭代的$ω（1/\ sqrt {t}）$的下限来证明此速率很紧。因此，该下限显示了在光滑的凸孔concave鞍点问题中的二次分离，最后迭代了。
In this paper we study the smooth convex-concave saddle point problem. Specifically, we analyze the last iterate convergence properties of the Extragradient (EG) algorithm. It is well known that the ergodic (averaged) iterates of EG converge at a rate of $O(1/T)$ (Nemirovski, 2004). In this paper, we show that the last iterate of EG converges at a rate of $O(1/\sqrt{T})$. To the best of our knowledge, this is the first paper to provide a convergence rate guarantee for the last iterate of EG for the smooth convex-concave saddle point problem. Moreover, we show that this rate is tight by proving a lower bound of $Ω(1/\sqrt{T})$ for the last iterate. This lower bound therefore shows a quadratic separation of the convergence rates of ergodic and last iterates in smooth convex-concave saddle point problems.
