9 research outputs found
Faster Gradient-Free Proximal Stochastic Methods for Nonconvex Nonsmooth Optimization
Proximal gradient method has been playing an important role to solve many
machine learning tasks, especially for the nonsmooth problems. However, in some
machine learning problems such as the bandit model and the black-box learning
problem, proximal gradient method could fail because the explicit gradients of
these problems are difficult or infeasible to obtain. The gradient-free
(zeroth-order) method can address these problems because only the objective
function values are required in the optimization. Recently, the first
zeroth-order proximal stochastic algorithm was proposed to solve the nonconvex
nonsmooth problems. However, its convergence rate is
for the nonconvex problems, which is significantly slower than the best
convergence rate of the zeroth-order stochastic algorithm,
where is the iteration number. To fill this gap, in the paper, we propose a
class of faster zeroth-order proximal stochastic methods with the variance
reduction techniques of SVRG and SAGA, which are denoted as ZO-ProxSVRG and
ZO-ProxSAGA, respectively. In theoretical analysis, we address the main
challenge that an unbiased estimate of the true gradient does not hold in the
zeroth-order case, which was required in previous theoretical analysis of both
SVRG and SAGA. Moreover, we prove that both ZO-ProxSVRG and ZO-ProxSAGA
algorithms have convergence rates. Finally, the experimental
results verify that our algorithms have a faster convergence rate than the
existing zeroth-order proximal stochastic algorithm.Comment: AAAI-2019, 22 page