论文标题
变异不平等方法的统一分析：降低方差，采样，量化和协调下降
A Unified Analysis of Variational Inequality Methods: Variance Reduction, Sampling, Quantization and Coordinate Descent
论文作者
论文摘要
在本文中，我们介绍了统一的分析，这些方法针对各种不平等等广泛问题，其中包括最小化问题和鞍点问题。我们对修改的额外梯度方法（用于变异不平等的经典算法）进行分析，并考虑强烈的单调和单调病例，该病例对应于强烈的convex-strong-rong-concove和凸孔conconcave鞍座点问题。理论分析基于有关梯度迭代的参数假设。因此，它可以作为结合已经存在的类型方法以及创建新算法的强大基础。特别是为了证明这一点，我们开发了新的鲁棒方法，其中包括具有量化的方法，坐标方法，分布式随机的本地方法等。这些方法中的大多数从未在变化不平等的一般性中被考虑过，并且以前仅用于最小化问题。新方法的鲁棒性也通过gan的数值实验证实。
In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient method (the classic algorithm for variational inequalities) and consider the strongly monotone and monotone cases, which corresponds to strongly-convex-strongly-concave and convex-concave saddle point problems. The theoretical analysis is based on parametric assumptions about Extra-Gradient iterations. Therefore, it can serve as a strong basis for combining the already existing type methods and also for creating new algorithms. In particular, to show this we develop new robust methods, which include methods with quantization, coordinate methods, distributed randomized local methods, and others. Most of these approaches have never been considered in the generality of variational inequalities and have previously been used only for minimization problems. The robustness of the new methods is also confirmed by numerical experiments with GANs.
