We study the convergence of the Proximal-Gradient algorithm for convex composite problems when both the gradient and the proximal mapping are computed approximately. This scenario occurs when the gradient is computationally expensive and the proximal operator is not available in closed form and may be computed only up to a certain fixed precision. We establish tight deterministic bounds and propose new probabilistic upper bounds on the suboptimality of the function values along the iterations under some statistical assumptions on the perturbed iterates. We use the Proximal-Gradient algorithm to solve randomly generated LASSO problems while varying the fixed-point machine representation and the proximal computation precision.
|Title of host publication
|2021 Sensor Signal Processing for Defence Conference (SSPD)
|Number of pages
|Published - 15 Sept 2021
|10th Sensor Signal Processing for Defence Conference 2021 - Edinburgh, United Kingdom
Duration: 14 Sept 2021 → 15 Sept 2021
|10th Sensor Signal Processing for Defence Conference 2021
|14/09/21 → 15/09/21
- Approximate Algorithms.
- Convex Optimization
- Proximal Gradient
ASJC Scopus subject areas
- Signal Processing
- Safety, Risk, Reliability and Quality