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Sharper Bounds for Proximal Gradient Algorithms with Errors. (arXiv:2203.02204v1 [math.OC])
March 7, 2022, 2:11 a.m. | Anis Hamadouche, Yun Wu, Andrew M. Wallace, Joao F. C. Mota
cs.LG updates on arXiv.org arxiv.org
We analyse the convergence of the proximal gradient algorithm for convex
composite problems in the presence of gradient and proximal computational
inaccuracies. We derive new tighter deterministic and probabilistic bounds that
we use to verify a simulated (MPC) and a synthetic (LASSO) optimization
problems solved on a reduced-precision machine in combination with an
inaccurate proximal operator. We also show how the probabilistic bounds are
more robust for algorithm verification and more accurate for application
performance guarantees. Under some statistical assumptions, …
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