Online and stochastic Douglas-Rachford splitting method for large scale machine learning
Provides the first sequential version of DRs for large-scale machine learning, but the regret bounds are standard and the contribution is incremental.
The paper generalizes Douglas-Rachford splitting to online and stochastic settings, achieving O(1) regret for online and O(1/√T) convergence for stochastic variants, with experiments confirming effectiveness.
Online and stochastic learning has emerged as powerful tool in large scale optimization. In this work, we generalize the Douglas-Rachford splitting (DRs) method for minimizing composite functions to online and stochastic settings (to our best knowledge this is the first time DRs been generalized to sequential version). We first establish an $O(1/\sqrt{T})$ regret bound for batch DRs method. Then we proved that the online DRs splitting method enjoy an $O(1)$ regret bound and stochastic DRs splitting has a convergence rate of $O(1/\sqrt{T})$. The proof is simple and intuitive, and the results and technique can be served as a initiate for the research on the large scale machine learning employ the DRs method. Numerical experiments of the proposed method demonstrate the effectiveness of the online and stochastic update rule, and further confirm our regret and convergence analysis.