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Lower Bound for Randomized First Order Convex Optimization

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arxiv 1709.03594 v2 pith:FZQYWMBE submitted 2017-09-11 math.OC

Blake Woodworth , Nathan Srebro This is my paper · ORCID
classification math.OC
keywords boundconvexfirstlowerorderrandomizedaccessesalgorithm
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We provide an explicit construction and direct proof for the lower bound on the number of first order oracle accesses required for a randomized algorithm to minimize a convex Lipschitz function.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Near-Optimal Lower Bounds for Randomized Algorithms in Exact Value Zeroth-Order Convex Optimization

    math.OC 2026-07 accept novelty 8.0 of 10

    Any randomized adaptive exact-value algorithm needs Ω(d min{d, ε^{-2}} / log(min{d, ε^{-2}})) queries for ε-optimal Lipschitz convex optimization, matching upper bounds up to log factors.

  2. The Adaptive Complexity of Finding a Stationary Point

    math.OC 2025-05 conditional novelty 7.0 of 10

    The adaptive round complexity of finding an epsilon-stationary point is Omega(epsilon^{-(p+1)/p}) in high dimension even with poly(d) parallel queries, and near-matching per-round query bounds are given in constant dimension.

  3. Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness

    cs.LG 2025-05 conditional novelty 7.0 of 10

    AdaGrad-type algorithms provably need a complexity quadratic in the initial gap and smoothness constants under relaxed smoothness, so they cannot match the optimal rate of clipped SGD.

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