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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2511.11517 |
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| _version_ | 1866917146353729536 |
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| author | Liu, Jitian Kozachuk, Nicolas Bhattacharya, Subhrajit |
| author_facet | Liu, Jitian Kozachuk, Nicolas Bhattacharya, Subhrajit |
| contents | We study distributed optimization of finite-degree polynomial Laplacian spectral objectives under fixed topology and a global weight budget, targeting the collective behavior of the entire spectrum rather than a few extremal eigenvalues. By re-formulating the global cost in a bilinear form, we derive local subgraph problems whose gradients approximately align with the global descent direction via an SVD-based test on the \(ZC\) matrix. This leads to an iterate-and-embed scheme over disjoint 1-hop neighborhoods that preserves feasibility by construction (positivity and budget) and scales to large geometric graphs. For objectives that depend on pairwise eigenvalue differences \(h(λ_i-λ_j)\), we obtain a quadratic upper bound in the degree vector, which motivates a ``warm-start'' by degree-regularization. The warm start uses randomized gossip to estimate global average degree, accelerating subsequent local descent while maintaining decentralization, and realizing $\sim95\%{}$ of the performance with respect to centralized optimization. We further introduce a learning-based proposer that predicts one-shot edge updates on maximal 1-hop embeddings, yielding immediate objective reductions. Together, these components form a practical, modular pipeline for spectrum-aware weight tuning that preserves constraints and applies across a broader class of whole-spectrum costs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed Optimization of Bivariate Polynomial Graph Spectral Functions via Subgraph Optimization Liu, Jitian Kozachuk, Nicolas Bhattacharya, Subhrajit Optimization and Control Social and Information Networks 05C90, 05C85 We study distributed optimization of finite-degree polynomial Laplacian spectral objectives under fixed topology and a global weight budget, targeting the collective behavior of the entire spectrum rather than a few extremal eigenvalues. By re-formulating the global cost in a bilinear form, we derive local subgraph problems whose gradients approximately align with the global descent direction via an SVD-based test on the \(ZC\) matrix. This leads to an iterate-and-embed scheme over disjoint 1-hop neighborhoods that preserves feasibility by construction (positivity and budget) and scales to large geometric graphs. For objectives that depend on pairwise eigenvalue differences \(h(λ_i-λ_j)\), we obtain a quadratic upper bound in the degree vector, which motivates a ``warm-start'' by degree-regularization. The warm start uses randomized gossip to estimate global average degree, accelerating subsequent local descent while maintaining decentralization, and realizing $\sim95\%{}$ of the performance with respect to centralized optimization. We further introduce a learning-based proposer that predicts one-shot edge updates on maximal 1-hop embeddings, yielding immediate objective reductions. Together, these components form a practical, modular pipeline for spectrum-aware weight tuning that preserves constraints and applies across a broader class of whole-spectrum costs. |
| title | Distributed Optimization of Bivariate Polynomial Graph Spectral Functions via Subgraph Optimization |
| topic | Optimization and Control Social and Information Networks 05C90, 05C85 |
| url | https://arxiv.org/abs/2511.11517 |