Accelerating nonconvex learning via replica exchange Langevin diffusion

Yi Chen, Jinglin Chen, Jing Dong, Jian Peng, Zhaoran Wang

Research output: Contribution to conferencePaperpeer-review

Abstract

Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient. In particular, the temperature parameter controlling the noise level gives rise to a tradeoff between “global exploration” and “local exploitation”, which correspond to high and low temperatures. To attain the advantages of both regimes, we propose to use replica exchange, which swaps between two Langevin diffusions with different temperatures. We theoretically analyze the acceleration effect of replica exchange from two perspectives: (i) the convergence in χ2-divergence, and (ii) the large deviation principle. Such an acceleration effect allows us to faster approach the global minima. Furthermore, by discretizing the replica exchange Langevin diffusion, we obtain a discrete-time algorithm. For such an algorithm, we quantify its discretization error in theory and demonstrate its acceleration effect in practice.

Original languageEnglish (US)
StatePublished - 2019
Event7th International Conference on Learning Representations, ICLR 2019 - New Orleans, United States
Duration: May 6 2019May 9 2019

Conference

Conference7th International Conference on Learning Representations, ICLR 2019
CountryUnited States
CityNew Orleans
Period5/6/195/9/19

ASJC Scopus subject areas

  • Education
  • Computer Science Applications
  • Linguistics and Language
  • Language and Linguistics

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