On the Perturbed Projection-Based Distributed Gradient-Descent Algorithm: A Fully-Distributed Adaptive Redesign
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918135108468736 |
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| author | Bazizi, Tarek Maghenem, Mohamed Frasca, Paolo Lorìa, Antonio Panteley, Elena |
| author_facet | Bazizi, Tarek Maghenem, Mohamed Frasca, Paolo Lorìa, Antonio Panteley, Elena |
| contents | In this work, we revisit a classical distributed gradient-descent algorithm, introducing an interesting class of perturbed multi-agent systems. The state of each subsystem represents a local estimate of a solution to the global optimization problem. Thereby, the network is required to minimize local cost functions, while gathering the local estimates around a common value. Such a complex task suggests the interplay of consensus-based dynamics with gradient-descent dynamics. The latter descent dynamics involves the projection operator, which is assumed to provide corrupted projections of a specific form, reminiscent of existing (fast) projection algorithms. Hence, for the resulting class of perturbed networks, we are able to adaptively tune some gains in a fully distributed fashion, to approach the optimal consensus set up to arbitrary-desired precision. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03443 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Perturbed Projection-Based Distributed Gradient-Descent Algorithm: A Fully-Distributed Adaptive Redesign Bazizi, Tarek Maghenem, Mohamed Frasca, Paolo Lorìa, Antonio Panteley, Elena Optimization and Control Systems and Control In this work, we revisit a classical distributed gradient-descent algorithm, introducing an interesting class of perturbed multi-agent systems. The state of each subsystem represents a local estimate of a solution to the global optimization problem. Thereby, the network is required to minimize local cost functions, while gathering the local estimates around a common value. Such a complex task suggests the interplay of consensus-based dynamics with gradient-descent dynamics. The latter descent dynamics involves the projection operator, which is assumed to provide corrupted projections of a specific form, reminiscent of existing (fast) projection algorithms. Hence, for the resulting class of perturbed networks, we are able to adaptively tune some gains in a fully distributed fashion, to approach the optimal consensus set up to arbitrary-desired precision. |
| title | On the Perturbed Projection-Based Distributed Gradient-Descent Algorithm: A Fully-Distributed Adaptive Redesign |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2509.03443 |