Lower Complexity Bounds for Finite-Sum Convex-Concave Minimax Optimization Problems
Authors: Guangzeng Xie, Luo Luo, Yijiang Lian, Zhihua Zhang
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper studies the lower bound complexity for minimax optimization problem whose objective function is the average of n individual smooth convex-concave functions. We consider the algorithm which has access to gradient and proximal oracle for each individual component. For the strongly-convex-strongly-concave case, we prove such an algorithm can not reach an ε-saddle point in fewer than Ω((n + κ) log(1/ε)) iterations, where κ is the condition number of the objective function. This lower bound matches the upper bound of the existing proximal incremental first-order oracle algorithm in some specific case. We develop a novel construction to show the above result, which partitions the tridiagonal matrix of classical examples into n groups. This construction is friendly to the analysis of incremental gradient and proximal oracle and we also extend the analysis to general convex-concave cases. |
| Researcher Affiliation | Collaboration | 1Academy for Advanced Interdisciplinary Studies, Peking University 2Department of Mathematics, Hong Kong University of Science and Technology 3Baidu Inc., Beijing 4School of Mathematical Sciences, Peking University 5Huawei Noah s Ark Lab, Beijing. |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code or links to a code repository for the methodology described. |
| Open Datasets | No | The paper is theoretical and does not describe experiments using datasets, thus there is no mention of publicly available or open datasets. |
| Dataset Splits | No | The paper is theoretical and does not describe experiments involving dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe any experiments that would require hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not describe any computational experiments that would require software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup details or hyperparameters. |