Sampling without Replacement Leads to Faster Rates in Finite-Sum Minimax Optimization

NeurIPS 2022(2022)

引用 5|浏览16
暂无评分
摘要
We analyze the convergence rates of stochastic gradient algorithms for smooth finite-sum minimax optimization and show that, for many such algorithms, sampling the data points without replacement leads to faster convergence compared to sampling with replacement. For the smooth and strongly convex-strongly concave setting, we consider gradient descent ascent and the proximal point method, and present a unified analysis of two popular without-replacement sampling strategies, namely Random Reshuffling (RR), which shuffles the data every epoch, and Single Shuffling or Shuffle Once (SO), which shuffles only at the beginning. We obtain tight convergence rates for RR and SO and demonstrate that these strategies lead to faster convergence than uniform sampling. Moving beyond convexity, we obtain similar results for smooth nonconvex-nonconcave objectives satisfying a two-sided Polyak-{\L}ojasiewicz inequality. Finally, we demonstrate that our techniques are general enough to analyze the effect of data-ordering attacks, where an adversary manipulates the order in which data points are supplied to the optimizer. Our analysis also recovers tight rates for the incremental gradient method, where the data points are not shuffled at all.
更多
查看译文
关键词
Minimax Optimization,Smooth Games,Nonconvex-Nonconcave Minimax Optimization,Sampling without Replacement,Random Reshuffling,Shuffle Once,Incremental Gradient,Gradient Descent Ascent,Proximal Point Method,Alternating Gradient Descent Ascent
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要