Regret analysis of an online majorized semi-proximal ADMM for online composite optimization

n online majorized semi-proximal alternating direction method of multiplier (Online-mspADMM) is proposed for a broad class of online linearly constrained composite optimization problems. A majorized technique is adopted to produce subproblems which can be easily solved. Under mild assumptions, we establish 𝒪(√(N)) objective regret and 𝒪(√(N)) constraint violation regret at round N . We apply the Online-mspADMM to solve different types of online regularized logistic regression problems. The numerical results on synthetic data sets verify the theoretical result about regrets.