{"paper":{"title":"A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A neural network predicts integer variables in parametric mixed-integer quadratic programs while a differentiable QP layer solves for the continuous part using a hybrid loss.","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Mu Xie, Rahul Mangharam, Viet-Anh Le","submitted_at":"2025-11-24T18:22:00Z","abstract_excerpt":"In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications. The framework learns to predict integer solutions with enhanced optimality and feasibility by integrating supervised learning (for optimality), self-supervised learning (for feasibility), and a differentiable quadratic programming (QP) layer, resulting in a hybrid L2O framework. Specifically, a neural network (NN) is used to learn the mapping from problem pa"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem's objective and constraints.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a neural network trained on a finite set of problem instances will produce integer predictions whose corresponding QP solutions remain near-optimal and feasible for unseen parameter values encountered at runtime.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A hybrid L2O framework predicts optimal integer solutions for MIQP via neural network, recovers continuous variables with a differentiable QP layer, and trains with supervised optimality loss plus self-supervised feasibility loss.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A neural network predicts integer variables in parametric mixed-integer quadratic programs while a differentiable QP layer solves for the continuous part using a hybrid loss.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"af752e1ae3388bd0eb5019d0306dd988e1c009573628d2d1712e831e017b9d50"},"source":{"id":"2511.19383","kind":"arxiv","version":2},"verdict":{"id":"c290aaae-dc86-4637-aec0-d4549c7582ba","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T05:03:37.746958Z","strongest_claim":"a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem's objective and constraints.","one_line_summary":"A hybrid L2O framework predicts optimal integer solutions for MIQP via neural network, recovers continuous variables with a differentiable QP layer, and trains with supervised optimality loss plus self-supervised feasibility loss.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a neural network trained on a finite set of problem instances will produce integer predictions whose corresponding QP solutions remain near-optimal and feasible for unseen parameter values encountered at runtime.","pith_extraction_headline":"A neural network predicts integer variables in parametric mixed-integer quadratic programs while a differentiable QP layer solves for the continuous part using a hybrid loss."},"references":{"count":15,"sample":[{"doi":"","year":2019,"title":"Differentiable convex optimization layers","work_id":"ca510b7c-a0b6-40ca-9fa7-cac50c47d76a","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Optnet: Differentiable optimization as a layer in neural networks","work_id":"fce385d6-ab8c-44d5-88d5-f8d8298677d5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Formal methods for control synthesis: An optimization perspective","work_id":"2e5e1d70-978b-4503-95b9-c8e94a3d8382","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation","work_id":"1fe8c7c8-aff7-4b94-9096-e549d7e60789","ref_index":4,"cited_arxiv_id":"1308.3432","is_internal_anchor":true},{"doi":"","year":2014,"title":"Constrained optimization and Lagrange multiplier methods","work_id":"f81857a8-6585-4fe3-bac3-fa9dc42f93d2","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":15,"snapshot_sha256":"069a3f05a0686efd4cb470aea340100084470e0206fbdf1af439df431966f126","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6f5ea609531c75bbd7d7b336d538fcc08504a4699bd96ba4aab66e9d3ab49188"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}