---
title: "On the Convergence of Stochastic Compositional Gradient Descent Ascent Method"
authors:
  - "Hongchang Gao"
  - "Xiaoqian Wang"
  - "Lei Luo"
  - "Xinghua Shi"
doi: "10.24963/ijcai.2021/329"
url: "https://ijcai.org/proceedings/2021/329"
pdf: "https://ijcai.org/proceedings/2021/0329.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "2389-2395"
track: "Main Track"
keywords:
  - "Machine Learning: Cost-Sensitive Learning"
  - "Machine Learning: Adversarial Machine Learning"
---

# On the Convergence of Stochastic Compositional Gradient Descent Ascent Method

Hongchang Gao, Xiaoqian Wang, Lei Luo, Xinghua Shi

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 2389-2395. DOI: [10.24963/ijcai.2021/329](https://doi.org/10.24963/ijcai.2021/329)

## Abstract

The compositional minimax problem covers plenty of machine learning models such as the distributionally robust compositional optimization problem. However,  it is yet another understudied problem to optimize the compositional minimax problem. In this paper, we develop a novel efficient stochastic compositional gradient descent ascent method for optimizing the compositional minimax problem. Moreover, we establish the theoretical convergence rate of our proposed method. To the best of our knowledge, this is the first work achieving such a convergence rate for the compositional minimax problem. Finally, we conduct extensive experiments to demonstrate the effectiveness of our proposed method.