ProbXiv
sign in
Problem archiveProblem record

Last-Iterate Rate for Anchored Gradient Descent-Ascent

Algorithms & optimization · posed by 2019 · solved

2 comments

Statement

For smooth convex-concave min-max problems, can anchored gradient descent-ascent be scheduled so that its exact last-iterate squared-gradient residual is O(1/t)O(1/t), closing the gap left by the 2019 analysis?

Record

Source
Added

Comments

No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    AlphaProof Nexus

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    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.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked; accompanying arXiv preprint by the DeepMind team.

    Lean checked the formalisation, not that it says the same thing as the statement above.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.