# K-Beam Minimax: Efficient Optimization for Deep Adversarial Learning

arXiv: https://arxiv.org/abs/1805.11640 · HTML: https://mlsanity.com/paper/1805.11640/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2018.

## Built on by (most cited first, 3 of 3)

- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [Uncertainty-Autoencoder-Based Privacy and Utility Preserving Data Type Conscious Transformation](https://mlsanity.com/paper/2205.01950/) (2022)
- [Learning for Robust Combinatorial Optimization: Algorithm and Application](https://mlsanity.com/paper/2112.10377/) (2021)

## Abstract (arXiv)

Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of alternating gradient descent in minimax optimization problems due to the discontinuity of solutions of the inner maximization. To address this, we propose a new epsilon-subgradient descent algorithm that addresses this problem by simultaneously tracking K candidate solutions. Practically, the algorithm can find solutions that previous saddle-point algorithms cannot find, with only a sublinear increase of complexity in K. We analyze the conditions under which the algorithm converges to the true solution in detail. A significant improvement in stability and convergence speed of the algorithm is observed in simple representative problems, GAN training, and domain-adaptation problems.