Polyak-style step sizes for Schedule-Free SGD and Adam achieve O(1/sqrt(t)) anytime last-iterate rates for convex Lipschitz problems using per-iteration loss and gradient information.
Analysis of schedule-free nonconvex optimization.arXiv preprint arXiv:2508.06743,
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Taking the Road Less Scheduled with Adaptive Polyak Steps
Polyak-style step sizes for Schedule-Free SGD and Adam achieve O(1/sqrt(t)) anytime last-iterate rates for convex Lipschitz problems using per-iteration loss and gradient information.