Accelerated Minimax Algorithms Flock Together
TaeHo Yoon, Ernest K. Ryu

TL;DR
This paper introduces the merging path property of accelerated minimax algorithms, proving their convergence and developing new algorithms with improved performance in strongly-convex-strongly-concave and prox-grad settings.
Contribution
It reveals the merging path property of accelerated minimax algorithms and leverages it to establish convergence and create new state-of-the-art algorithms.
Findings
Algorithms exhibit rapid merging trajectories
Proven convergence of existing accelerated minimax methods
New algorithms outperform previous methods in key setups
Abstract
Several new accelerated methods in minimax optimization and fixed-point iterations have recently been discovered, and, interestingly, they rely on a mechanism distinct from Nesterov's momentum-based acceleration. In this work, we show that these accelerated algorithms exhibit what we call the merging path (MP) property; the trajectories of these algorithms merge quickly. Using this novel MP property, we establish point convergence of existing accelerated minimax algorithms and derive new state-of-the-art algorithms for the strongly-convex-strongly-concave setup and for the prox-grad setup.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSparse and Compressive Sensing Techniques · Advanced Optimization Algorithms Research · Stochastic Gradient Optimization Techniques
