论文标题
收敛性和尺寸无关的最低最大最大优化算法
A Convergent and Dimension-Independent Min-Max Optimization Algorithm
论文作者
论文摘要
我们研究了最近引入的最低最大优化框架的变体，其中最大玩具被限制以贪婪的方式更新其参数，直到达到一阶固定点为止。我们对此框架的均衡定义取决于最小玩家使用该方向来更新其参数的方向的提案分布。我们表明，鉴于一个平滑且有限的非Convex-Nonconcave目标函数，可以访问Min-player的更新的任何提案分布，以及Max-player的随机梯度甲骨文，我们的算法会收敛到上述近似局部平衡的局部均衡，这些局部平衡不依赖于压损。我们的算法发现的平衡点取决于提议分布，在应用我们的算法训练gans时，我们选择提案分布作为随机梯度的分布。我们从经验上评估了我们的算法，以挑战非凸孔测试功能和GAN训练中引起的损失功能。我们的算法在这些测试功能上收敛，并在用于训练gan时会稳定地训练合成和现实世界数据集，并避免模式崩溃
We study a variant of a recently introduced min-max optimization framework where the max-player is constrained to update its parameters in a greedy manner until it reaches a first-order stationary point. Our equilibrium definition for this framework depends on a proposal distribution which the min-player uses to choose directions in which to update its parameters. We show that, given a smooth and bounded nonconvex-nonconcave objective function, access to any proposal distribution for the min-player's updates, and stochastic gradient oracle for the max-player, our algorithm converges to the aforementioned approximate local equilibrium in a number of iterations that does not depend on the dimension. The equilibrium point found by our algorithm depends on the proposal distribution, and when applying our algorithm to train GANs we choose the proposal distribution to be a distribution of stochastic gradients. We empirically evaluate our algorithm on challenging nonconvex-nonconcave test-functions and loss functions arising in GAN training. Our algorithm converges on these test functions and, when used to train GANs, trains stably on synthetic and real-world datasets and avoids mode collapse
