TY - GEN
T1 - Local Convergence Properties of SAGA/Prox-SVRG and Acceleration
AU - Poon, Clarice
AU - Liang, Jingwei
AU - Schoenlieb, Carola
PY - 2018/10/1
Y1 - 2018/10/1
N2 - In this paper, we present a local convergence anal- ysis for a class of stochastic optimisation meth- ods: the proximal variance reduced stochastic gradient methods, and mainly focus on SAGA (Defazio et al., 2014) and Prox-SVRG (Xiao & Zhang, 2014). Under the assumption that the non-smooth component of the optimisation prob- lem is partly smooth relative to a smooth mani- fold, we present a unified framework for the local convergence analysis of SAGA/Prox-SVRG: (i) the sequences generated by the methods are able to identify the smooth manifold in a finite num- ber of iterations; (ii) then the sequence enters a local linear convergence regime. Furthermore, we discuss various possibilities for accelerating these algorithms, including adapting to better lo- cal parameters, and applying higher-order deter- ministic/stochastic optimisation methods which can achieve super-linear convergence. Several concrete examples arising from machine learning are considered to demonstrate the obtained result.
AB - In this paper, we present a local convergence anal- ysis for a class of stochastic optimisation meth- ods: the proximal variance reduced stochastic gradient methods, and mainly focus on SAGA (Defazio et al., 2014) and Prox-SVRG (Xiao & Zhang, 2014). Under the assumption that the non-smooth component of the optimisation prob- lem is partly smooth relative to a smooth mani- fold, we present a unified framework for the local convergence analysis of SAGA/Prox-SVRG: (i) the sequences generated by the methods are able to identify the smooth manifold in a finite num- ber of iterations; (ii) then the sequence enters a local linear convergence regime. Furthermore, we discuss various possibilities for accelerating these algorithms, including adapting to better lo- cal parameters, and applying higher-order deter- ministic/stochastic optimisation methods which can achieve super-linear convergence. Several concrete examples arising from machine learning are considered to demonstrate the obtained result.
M3 - Chapter in a published conference proceeding
VL - 80
T3 - Proceedings of Machine Learning Research
SP - 4124
EP - 4132
BT - Proceedings of the 35th International Conference on Machine Learning
A2 - Dy, Jennifer
A2 - Krause, Andreas
PB - PMLR
CY - Stockholmsmässan, Stockholm Sweden
ER -