TY - JOUR
T1 - On Linear Convergence of ADMM for Decentralized Quantile Regression
AU - Wang, Yue
AU - Lian, Heng
PY - 2023
Y1 - 2023
N2 - The alternating direction method of multipliers (ADMM) is a natural method of choice for distributed parameter learning. For smooth and strongly convex consensus optimization problems, it has been shown that ADMM and some of its variants enjoy linear convergence in the distributed setting, much like in the traditional non-distributed setting. The optimization problem associated with parameter estimation in quantile regression is neither smooth nor strongly convex (although is convex) and thus it seems can only have sublinear convergence at best. Although this insinuates slow convergence, we show that, if the local sample size is sufficiently large compared to parameter dimension and network size, distributed estimation in quantile regression actually exhibits linear convergence up to the statistical precision, the precise meaning of which will be explained in the text. © 2023 IEEE.
AB - The alternating direction method of multipliers (ADMM) is a natural method of choice for distributed parameter learning. For smooth and strongly convex consensus optimization problems, it has been shown that ADMM and some of its variants enjoy linear convergence in the distributed setting, much like in the traditional non-distributed setting. The optimization problem associated with parameter estimation in quantile regression is neither smooth nor strongly convex (although is convex) and thus it seems can only have sublinear convergence at best. Although this insinuates slow convergence, we show that, if the local sample size is sufficiently large compared to parameter dimension and network size, distributed estimation in quantile regression actually exhibits linear convergence up to the statistical precision, the precise meaning of which will be explained in the text. © 2023 IEEE.
KW - ADMM
KW - linear convergence
KW - proximal operator
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U2 - 10.1109/TSP.2023.3325622
DO - 10.1109/TSP.2023.3325622
M3 - RGC 21 - Publication in refereed journal
VL - 71
SP - 3945
EP - 3955
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
ER -