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Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds #6

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nocotan opened this issue Dec 30, 2020 · 0 comments
Open

Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds #6

nocotan opened this issue Dec 30, 2020 · 0 comments
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riemannian optimization

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nocotan commented Dec 30, 2020

一言でいうと

分散緩和のリーマン確率的最適化の手法であるRiemannian SVRG (RSVRG)を提案．

論文リンク

NeurIPS2016:
https://papers.nips.cc/paper/2016/file/98e6f17209029f4ae6dc9d88ec8eac2c-Paper.pdf

著者/所属機関

Hongyi Zhang (MIT), Sashank J. Reddi (Carnegie Mellon University), Suvrit Sra (MIT)

投稿日付(yyyy/MM/dd)

2016/05/23

概要

以下のようなリーマン多様体(M,g)の上の有限和最適化問題を扱う．
Screen Shot 2020-12-30 at 23 18 07

この問題について，分散緩和のリーマン確率的最適化の手法であるRiemannian SVRG (RSVRG)を提案．

Screen Shot 2020-12-30 at 23 30 41

新規性・差分

測地的強凸な関数の大域的線形収束レートと、測地的非凸な最適化のための一次非漸近収束レートを備えた最初の確率的勾配法を提案

手法

Screen Shot 2020-12-30 at 23 31 14

Screen Shot 2020-12-30 at 23 31 35

結果

Screen Shot 2020-12-30 at 23 32 22

Screen Shot 2020-12-30 at 23 32 42

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