Approximate Proximal-Gradient Methods
Published in 2021 Sensor Signal Processing for Defence Conference (SSPD): Proceedings, 2021
This paper investigates the convergence of the Proximal-Gradient algorithm for convex composite problems when both the gradient and the proximal mapping are computed approximately. This scenario arises when the gradient is computationally expensive and the proximal operator is not available in closed form, necessitating approximate computations.
Key contributions include:
Convergence Analysis: The authors establish tight deterministic bounds and propose new probabilistic upper bounds on the suboptimality of the function values along the iterations under certain statistical assumptions on the perturbed iterates.
Empirical Evaluation: The Proximal-Gradient algorithm is applied to solve randomly generated LASSO problems, varying the fixed-point machine representation and the proximal computation precision to assess the impact on performance.
Practical Implications: The findings highlight the trade-offs between computational efficiency and solution accuracy, providing insights for implementing approximate proximal-gradient methods in resource-constrained environments.
Recommended citation: Hamadouche, A., Wu, Y., Wallace, A. M., & Mota, J. F. C. (2021). Approximate Proximal-Gradient Methods. In *Proceedings of the 2021 Sensor Signal Processing for Defence Conference (SSPD)*. IEEE. https://doi.org/10.1109/SSPD51364.2021.9541509
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