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math.OCSep 1, 2017
14
citations (OpenAlex)
authors
  • Blake Woodworth
  • Nathan Srebro
arXiv abstractPDF
paper

Lower Bound for Randomized First Order Convex Optimization

arXiv:1709.03594

Abstract

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.

8 pages

References in corpus (1)

  • Tight Complexity Bounds for Optimizing Composite Objectives

Cited by in corpus (11)

  • SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator
  • Tight Complexity Bounds for Optimizing Composite Objectives
  • Calibration for the (Computationally-Identifiable) Masses
  • Can We Find Near-Approximately-Stationary Points of Nonsmooth Nonconvex Functions?
  • Acceleration with a Ball Optimization Oracle
  • Oracle Complexity in Nonsmooth Nonconvex Optimization
  • The gradient complexity of linear regression
  • High-Order Oracle Complexity of Smooth and Strongly Convex Optimization
  • The Minimax Complexity of Distributed Optimization
  • Open Problem: The Oracle Complexity of Convex Optimization with Limited Memory
  • Big-Step-Little-Step: Efficient Gradient Methods for Objectives with Multiple Scales
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