Optimization of Random High-Dimensional Functions: Structure and Algorithms

Antonio Auffinger, Andrea Montanariy, Eliran Subagz

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated with leaves of a tree, and the Euclidean distance between them corresponds to the distance along this tree. We survey recent progress toward a rigorous proof of this picture in the context of mixed p-spin spin glass models. We focus in particular on the following topics: (i) The structure of critical points of the Hamiltonian; (ii) The realization of the ultrametric tree as near optima of a suitable TAP free energy; (iii) The construction of an efficient optimization algorithm that exploits this picture.

Original languageEnglish
Title of host publicationSpin Glass Theory and Far Beyond
Subtitle of host publicationReplica Symmetry Breaking after 40 Years
PublisherWorld Scientific Publishing Co.
Chapter29
Pages609-633
Number of pages25
ISBN (Electronic)9789811273926
ISBN (Print)9789811273919
DOIs
StatePublished - 1 Jan 2023

All Science Journal Classification (ASJC) codes

  • General Engineering
  • General Physics and Astronomy

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