{"ID":2841850,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11517","arxiv_id":"2511.11517","title":"Distributed Optimization of Bivariate Polynomial Graph Spectral Functions via Subgraph Optimization","abstract":"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.","short_abstract":"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 pro...","url_abs":"https://arxiv.org/abs/2511.11517","url_pdf":"https://arxiv.org/pdf/2511.11517v2","authors":"[\"Jitian Liu\",\"Nicolas Kozachuk\",\"Subhrajit Bhattacharya\"]","published":"2025-11-14T17:42:00Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.SI\"]","methods":"[]","has_code":false}