SCIENCE@home

Stochastic Subspace Descent

D. Kozak,Stephen Becker,A. Doostan,L. Tenorio

Published 2019 in arXiv: Optimization and Control

ABSTRACT

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and machine learning problems. The basic algorithm projects the gradient onto a random subspace at each iteration, similar to coordinate descent but without restricting directional derivatives to be along the axes. This algorithm is previously known but we provide new analysis. We also extend the popular SVRG method to this framework but without requiring that the objective function be written as a finite sum. We provide proofs of convergence for our methods under various convexity assumptions and show favorable results when compared to gradient descent and BFGS on non-convex problems from the machine learning and shape optimization literature. We also note that our analysis gives a proof that the iterates of SVRG and several other popular first-order stochastic methods, in their original formulation, converge almost surely to the optimum; to our knowledge, prior to this work the iterates of SVRG had only been known to converge in expectation.

PUBLICATION RECORD

  • Publication year

    2019

  • Venue

    arXiv: Optimization and Control

  • Publication date

    2019-04-01

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 1904.01145
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-99 of 99 references · Page 1 of 1

CITED BY

Showing 1-30 of 30 citing papers · Page 1 of 1