TY - JOUR
T1 - Extended Regularized Dual Averaging Methods for Stochastic Optimization
AU - Siegel , Jonathan W.
AU - Xu , Jinchao
JO - Journal of Computational Mathematics
VL - 3
SP - 525
EP - 541
PY - 2023
DA - 2023/04
SN - 41
DO - http://doi.org/10.4208/jcm.2210-m2021-0106
UR - https://global-sci.org/intro/article_detail/jcm/21637.html
KW - Convex Optimization, Subgradient Methods, Structured Optimization, Non-smooth Optimization.
AB - <p>We introduce a new algorithm, extended regularized dual averaging (XRDA), for solving regularized stochastic optimization problems, which generalizes the regularized dual averaging (RDA) method. The main novelty of the method is that it allows a flexible control of the backward step size. For instance, the backward step size used in RDA grows without bound, while for XRDA the backward step size can be kept bounded. We demonstrate experimentally that additional control over the backward step size can speed up the convergence of the algorithm while preserving desired properties of the iterates, such as sparsity. Theoretically, we show that the XRDA method achieves the same convergence rate as RDA for general convex objectives.</p>