488. Steering Towards Success: Efficient Methods for Nonconvex-Nonconcave Minimax Problems
Invited abstract in session WB-5: Recent advances in min-max optimization, stream Optimization for machine learning.
Wednesday, 10:30-12:30Room: B100/4013
Authors (first author is the speaker)
| 1. | Pontus Giselsson
|
| Dept. of Automatic Control, Lund University | |
| 2. | Anton Åkerman
|
| Department of Automatic Control, Lund University | |
| 3. | Max Nilsson
|
| Department of Automatic Control, Lund University | |
| 4. | Manu Upadhyaya
|
| Lund University | |
| 5. | Sebastian Banert
|
| Uni Bremen |
Abstract
Nonconvex-nonconcave minimax problems frequently arise in applications, yet finding even a first-order stationary point is generally intractable without additional structure. The recently introduced Weak Minty variational inequality framework imposes such structure, enabling specialized extragradient-type methods with global convergence guarantees. Building on one of them, AdaptiveEG+, we propose three new algorithms that retain the same global convergence guarantees. One integrates momentum, while the other two incorporate Anderson acceleration directions through a novel one-shot line search strategy to combine the global convergence of AdaptiveEG+ with the fast local convergence of Anderson acceleration. All three methods derive from our new D-FLEX framework for solving firmly quasinonexpansive fixed-point problems, which leverages steering vectors to enhance practical performance. Indeed, numerical experiments showcase superior performance for the proposed methods on some challenging nonconvex-nonconcave minimax problems.
Keywords
- First-order optimization
- Monotone inclusion problems
- Non-smooth optimization
Status: accepted
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