{"doi":"10.48550/arxiv.2512.02494","title":"A Fully First-Order Layer for Differentiable Optimization","abstract":"Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems. However, computing gradients via implicit differentiation requires solving a linear system with Hessian terms, which is both compute- and memory-intensive. To address this challenge, we propose a novel algorithm that computes the gradient using only first-order information. The key insight is to rewrite the differentiable optimization as a bilevel optimization problem and leverage recent advances in bilevel methods. Specifically, we introduce an active-set Lagrangian hypergradient oracle that avoids Hessian evaluations and provides finite-time, non-asymptotic approximation guarantees. We show that an approximate hypergradient can be computed using only first-order information in $\\tilde{O}(1)$ time, leading to an overall complexity of $\\tilde{O}(δ^{-1}ε^{-3})$ for constrained bilevel optimization, which matches the best known rate for non-smooth non-convex optimization. Furthermore, we release an open-source Python library that can be easily adapted from existing solvers. The source code is available at https://github.com/guaguakai/FFOLayer.","journal":"arXiv (Cornell University)","year":2025,"id":584211,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9487,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2025-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1497510,"name":"Kai-Chia Mo","orcid":null,"position":1,"is_corresponding":false},{"id":1497099,"name":"Shu‐peng Ho","orcid":"0000-0002-3010-8544","position":2,"is_corresponding":false},{"id":1497100,"name":"Brandon Amos","orcid":"0000-0003-2884-0119","position":3,"is_corresponding":false},{"id":1428089,"name":"Kai Wang","orcid":"0000-0002-1171-0281","position":4,"is_corresponding":false},{"id":1497098,"name":"Zihao Zhao","orcid":"0000-0001-7173-3226","position":0,"is_corresponding":true}],"reference_count":0,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-07-19T02:59:11.978098Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}