论文标题
带有动态不精确的梯度方法
Gradient Methods with Dynamic Inexact Oracles
论文作者
论文摘要
我们表明，用于求解凸孔conconcove minimax问题的原始双重梯度方法（也称为梯度下降方法）可以看作是应用于原始问题的一种不精确梯度方法。该梯度的确切计算依赖于解决内部最大化问题的梯度大约通过另一种梯度方法计算。为了建模由迭代算法实现的近似计算例程，我们介绍了动态不凝聚力的概念，该概念是离散的时间动态系统，其输出渐近地接近了精确的Oracle的输出。我们提出了通过一般一阶方法实现的动态不精确的统一收敛分析，并证明了其在创建新的加速原始偶算算法中的用途。
We show that the primal-dual gradient method, also known as the gradient descent ascent method, for solving convex-concave minimax problems can be viewed as an inexact gradient method applied to the primal problem. The gradient, whose exact computation relies on solving the inner maximization problem, is computed approximately by another gradient method. To model the approximate computational routine implemented by iterative algorithms, we introduce the notion of dynamic inexact oracles, which are discrete-time dynamical systems whose output asymptotically approaches the output of an exact oracle. We present a unified convergence analysis for dynamic inexact oracles realized by general first-order methods and demonstrate its use in creating new accelerated primal-dual algorithms.
