Computer-Assisted Design of Accelerated Composite Optimization Methods: OptISTA
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| Publicado en: | arXiv.org (Sep 14, 2024), p. n/a |
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| Autor principal: | |
| Otros Autores: | , |
| Publicado: |
Cornell University Library, arXiv.org
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| Materias: | |
| Acceso en línea: | Citation/Abstract Full text outside of ProQuest |
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| Resumen: | The accelerated composite optimization method FISTA (Beck, Teboulle 2009) is suboptimal, and we present a new method OptISTA that improves upon it by a factor of 2. The performance estimation problem (PEP) has recently been introduced as a new computer-assisted paradigm for designing optimal first-order methods, but the methodology was largely limited to unconstrained optimization with a single function. In this work, we present a novel double-function stepsize-optimization PEP methodology that poses the optimization over fixed-step first-order methods for composite optimization as a finite-dimensional nonconvex QCQP, which can be practically solved through spatial branch-and-bound algorithms, and use it to design the exact optimal method OptISTA for the composite optimization setup. We then establish the exact optimality of OptISTA with a novel lower-bound construction that extends the semi-interpolated zero-chain construction (Drori, Taylor 2022) to the double-function setup of composite optimization. By establishing exact optimality, our work concludes the search for the fastest first-order methods for the proximal, projected-gradient, and proximal-gradient setups. |
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| ISSN: | 2331-8422 |
| Fuente: | Engineering Database |