Stochastic Dual Coordinate Ascent with Alternating Direction Multiplier Method
This work provides a stochastic optimization method for machine learning practitioners dealing with structured regularization, though it appears incremental as it adapts existing ADMM techniques to a stochastic setting.
The authors tackled the problem of applying stochastic updates to regularized learning problems with complex regularization functions by developing a stochastic dual coordinate ascent method based on ADMM, which converges exponentially under mild assumptions and performs efficiently in numerical experiments.
We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization functions such as structured regularizations. Although the original ADMM is a batch method, the proposed method offers a stochastic update rule where each iteration requires only one or few sample observations. Moreover, our method can naturally afford mini-batch update and it gives speed up of convergence. We show that, under mild assumptions, our method converges exponentially. The numerical experiments show that our method actually performs efficiently.