Online Alternating Direction Method
This work addresses online optimization challenges for large-scale applications, presenting incremental improvements with new regret bounds.
The paper tackles the problem of large-scale online optimization by introducing efficient online algorithms based on the alternating directions method (ADM), establishing regret bounds for objective function and constraint violation in general and strongly convex functions, with preliminary results illustrating performance.
Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online algorithms based on the alternating directions method (ADM). We introduce a new proof technique for ADM in the batch setting, which yields the O(1/T) convergence rate of ADM and forms the basis of regret analysis in the online setting. We consider two scenarios in the online setting, based on whether the solution needs to lie in the feasible set or not. In both settings, we establish regret bounds for both the objective function as well as constraint violation for general and strongly convex functions. Preliminary results are presented to illustrate the performance of the proposed algorithms.