A stochastic variance reduction algorithm with Bregman distances for structured composite problems

Abstract

We develop a novel stochastic primal–dual splitting method with Bregman distances for solving structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the primal–dual gap is proved under mild conditions on stepsize for the general case. The linear convergence rate is obtained under additional condition like the strong convexity relative to Bregman functions.

Keywords:

• Stochastic optimization
• variance reduction
• Bregman distance
• reflected method
• primal–dual algorithm
• Ergodic convergence
• linear convergence

2010 Mathematics Subject Classifications:

• 49M29
• 65K10
• 65Y20
• 90C25

Acknowledgments

The authors thank the reviewers for their careful reading of the paper, their suggestions to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is funded by University of Transport and Communications (UTC) under grant number T2022-CB-008.