Anderson Acceleration of Proximal Gradient Methods
This work addresses optimization efficiency for machine learning and computational fields, but it is incremental as it extends existing techniques to new problem classes.
The authors tackled the problem of accelerating proximal gradient methods for non-smooth and constrained optimization by adapting Anderson acceleration, achieving local convergence under technical conditions and proposing a stabilization scheme to combine global guarantees with practical speed-up.
Anderson acceleration is a well-established and simple technique for speeding up fixed-point computations with countless applications. Previous studies of Anderson acceleration in optimization have only been able to provide convergence guarantees for unconstrained and smooth problems. This work introduces novel methods for adapting Anderson acceleration to (non-smooth and constrained) proximal gradient algorithms. Under some technical conditions, we extend the existing local convergence results of Anderson acceleration for smooth fixed-point mappings to the proposed scheme. We also prove analytically that it is not, in general, possible to guarantee global convergence of native Anderson acceleration. We therefore propose a simple scheme for stabilization that combines the global worst-case guarantees of proximal gradient methods with the local adaptation and practical speed-up of Anderson acceleration.