Pu, Wei;
Eldar, Yonina C;
Rodrigues, Miguel RD;
(2022)
Optimization Guarantees for ISTA and ADMM Based Unfolded Networks.
In:
2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).
(pp. pp. 8687-8691).
IEEE
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Abstract
Recently, unfolding techniques have been widely utilized to solve the inverse problems in various applications. In this paper, we study optimization guarantees for two popular unfolded networks, i.e., unfolded networks derived from iterative soft thresholding algorithms (ISTA) and derived from Alternating Direction Method of Multipliers (ADMM). Our guarantees–leveraging the Polyak-Lojasiewicz* (PL*) condition–state that the training (empirical) loss decreases to zero with the increase in the number of gradient descent epochs provided that the number of training samples is less than some threshold that depends on various quantities underlying the desired information processing task. Our guarantees also show that this threshold is larger for unfolded ISTA in comparison to unfolded ADMM, suggesting that there are certain regimes of number of training samples where the training error of unfolded ADMM does not converge to zero whereas the training error of unfolded ISTA does. A number of numerical results are provided backing up our theoretical findings.
| Type: | Proceedings paper |
|---|---|
| Title: | Optimization Guarantees for ISTA and ADMM Based Unfolded Networks |
| Event: | 47th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |
| Location: | Singapore, SINGAPORE |
| Dates: | 22 May 2022 - 27 May 2022 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/ICASSP43922.2022.9746860 |
| Publisher version: | https://doi.org/10.1109/ICASSP43922.2022.9746860 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Acoustics, ALGORITHM, Algorithm unfolding, Computer Science, Computer Science, Artificial Intelligence, Engineering, Engineering, Electrical & Electronic, optimization guarantee, Polyak-Lojasiewicz* (PL*) condition, Science & Technology, SIGNAL, Technology |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10172101 |
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