# Efficient Projection-Free Algorithms for Saddle Point Problems

arXiv: https://arxiv.org/abs/2010.11737 · HTML: https://mlsanity.com/paper/2010.11737/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [Decentralized Stochastic Gradient Descent Ascent for Finite-Sum Minimax Problems](https://mlsanity.com/paper/2212.02724/) (2022)
- [A Survey of Decision Making in Adversarial Games](https://mlsanity.com/paper/2207.07971/) (2022)
- [Non-Expansive Mappings in Two-Time-Scale Stochastic Approximation: Finite-Time Analysis](https://mlsanity.com/paper/2501.10806/) (2025)
- [Projection-Free Functional Constrained Optimization for Risk Aversion and Sparsity Control](https://mlsanity.com/paper/2210.05108/) (2022)
- [Faster Stochastic Variance Reduction Methods for Compositional MiniMax Optimization](https://mlsanity.com/paper/2308.09604/) (2023)
- [Federated Composite Saddle Point Optimization](https://mlsanity.com/paper/2305.15643/) (2023)

## Abstract (arXiv)

The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper, we study projection-free algorithms for convex-strongly-concave saddle point problems with complicated constraints. Our method combines Conditional Gradient Sliding with Mirror-Prox and shows that it only requires tildeO(1/√ε) gradient evaluations and tildeO(1/ε2) linear optimizations in the batch setting. We also extend our method to the stochastic setting and propose first stochastic projection-free algorithms for saddle point problems. Experimental results demonstrate the effectiveness of our algorithms and verify our theoretical guarantees.