A Provably Convergent and Practical Algorithm for Min-Max Optimization with Applications to GANs
Bibliographic record
Abstract
We present a first-order algorithm for nonconvex-nonconcave min-max optimization problems such as those that arise in training GANs. Our algorithm provably converges in poly(d,L,b) steps for any loss function f:Rd×Rd→R which is b-bounded with L-Lipschitz gradient. To achieve convergence, we 1) give a novel approximation to the global strategy of the max-player based on first-order algorithms such as gradient ascent, and 2) empower the min-player to look ahead and simulate the max-player’s response for arbitrarily many steps, but restrict the min-player to move according to updates sampled from a stochastic gradient oracle. Our algorithm, when used to train GANs on synthetic and real-world datasets, does not cycle, results in GANs that seem to avoid mode collapse, and achieves a training time per iteration and memory requirement similar to gradient descent-ascent.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".