Glocal smoothness enables iterate-independent complexity bounds showing line search and adaptive steps outperform fixed steps, with GD+line search sometimes beating accelerated GD.
Initialized at wtδ, using lemma 25 with¯L = L∗, we have thatL∗ 2 ∥wt − w∗∥2 ≤ ϵ after an additional t = ⌈ 4L∗ µ log L∗ 2 ∥wtδ −w∗∥2 ϵ ⌉ iterations
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Glocal Smoothness: Line search and adaptive step sizes can help in theory too!
Glocal smoothness enables iterate-independent complexity bounds showing line search and adaptive steps outperform fixed steps, with GD+line search sometimes beating accelerated GD.