Last-Iterate Rate for Anchored Gradient Descent-Ascent
For smooth convex-concave min-max problems, can anchored gradient descent-ascent be scheduled so that its exact last-iterate squared-gradient residual is , closing the gap left by the 2019 analysis?
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Convex optimization
- Posed by
- —
- Year posed
- 2019
- Years open
- 7y
- Solved
- 2026-04-04
- Model
- AlphaProof Nexus
- Vendor
- Google DeepMind
- Collaborators
- —
- Verification
- Lean-verified
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The agent searched for the anchoring schedule and its proof simultaneously, discovering a parameter choice yielding the stronger guarantee via a discrete-time recurrence argument rather than the usual continuous-time ODE analysis.
Verification
Lean-checked; accompanying arXiv preprint by the DeepMind team.
Source
arXiv:2604.03782 - An improved last-iterate convergence rate for anchored gradient descent ascent