{"ID":2875093,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.03443","arxiv_id":"2509.03443","title":"On the Perturbed Projection-Based Distributed Gradient-Descent Algorithm: A Fully-Distributed Adaptive Redesign","abstract":"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.","short_abstract":"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, whi...","url_abs":"https://arxiv.org/abs/2509.03443","url_pdf":"https://arxiv.org/pdf/2509.03443v1","authors":"[\"Tarek Bazizi\",\"Mohamed Maghenem\",\"Paolo Frasca\",\"Antonio Lorìa\",\"Elena Panteley\"]","published":"2025-09-03T16:11:30Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}