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 atwtδ, using Corollary 30 and Lemma 29 with ¯L = L∗, we have thatE[f(wt) | Xδ] − f∗ ≤ ϵ after another t = ⌈ dL∗ µ log f(wtδ )−f∗ 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.