On stochastic mirror descent with interacting particles: Convergence properties and variance reduction

PHYSICA D-NONLINEAR PHENOMENA

卷:418

Article

Borovykh, A.¹  Kantas, N.²  Parpas, P.¹  Pavliotis, G. A.² 

[1] Imperial Coll London, Dept Comp, London, England

[2] Imperial Coll London, Dept Math, London, England

关键词: Mirror descent;    Interacting agents;    Variance reduction;   

DOI  :  10.1016/j.physd.2021.132844

来源: Elsevier

【 摘 要 】

An open problem in optimization with noisy information is the computation of an exact minimizer that is independent of the amount of noise. A standard practice in stochastic approximation algorithms is to use a decreasing step-size. This however leads to a slower convergence. A second alternative is to use a fixed step-size and run independent replicas of the algorithm and average these. A third option is to run replicas of the algorithm and allow them to interact. It is unclear which of these options works best. To address this question, we reduce the problem of the computation of an exact minimizer with noisy gradient information to the study of stochastic mirror descent with interacting particles. We study the convergence of stochastic mirror descent and make explicit the tradeoffs between communication and variance reduction. We provide theoretical and numerical evidence to suggest that interaction helps to improve convergence and reduce the variance of the estimate. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free