Article ; Online: A Hamilton-Jacobi-based proximal operator.
Proceedings of the National Academy of Sciences of the United States of America
2023 Volume 120, Issue 14, Page(s) e2220469120
Abstract: First-order optimization algorithms are widely used today. Two standard building blocks in these algorithms are proximal operators (proximals) and gradients. Although gradients can be computed for a wide array of functions, explicit proximal formulas are ...
Abstract | First-order optimization algorithms are widely used today. Two standard building blocks in these algorithms are proximal operators (proximals) and gradients. Although gradients can be computed for a wide array of functions, explicit proximal formulas are known for only limited classes of functions. We provide an algorithm, HJ-Prox, for accurately approximating such proximals. This is derived from a collection of relations between proximals, Moreau envelopes, Hamilton-Jacobi (HJ) equations, heat equations, and Monte Carlo sampling. In particular, HJ-Prox smoothly approximates the Moreau envelope and its gradient. The smoothness can be adjusted to act as a denoiser. Our approach applies even when functions are accessible only by (possibly noisy) black box samples. We show that HJ-Prox is effective numerically via several examples. |
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Language | English |
Publishing date | 2023-03-29 |
Publishing country | United States |
Document type | Journal Article |
ZDB-ID | 209104-5 |
ISSN | 1091-6490 ; 0027-8424 |
ISSN (online) | 1091-6490 |
ISSN | 0027-8424 |
DOI | 10.1073/pnas.2220469120 |
Database | MEDical Literature Analysis and Retrieval System OnLINE |
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