Variable Metric Proximal Gradient Method With Diagonal Barzilai-Borwein Stepsize

This paper proposes an adaptive metric selection strategy called diagonal Barzilai-Borwein (DBB) stepsize for the popular Variable Metric Proximal Gradient (VM-PG) algorithm. The proposed approach better captures the local geometry of the problem while keeping the per-step computation cost similar to the widely used scalar Barzilai-Borwein (BB) stepsize. We provide the theoretical convergence analysis for VM-PG using DBB stepsize. Finally, our empirical results shows ~10 - 40 % improvement in convergence times for the VM-PG using DBB compared to the BB stepsize for different machine learning problems on several datasets.