{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/faster-predict-and-optimize-with-three","title":"Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splitting","arxiv_id":"2301.13395","date":"2023-01-31","proceeding":null,"authors":["Daniel Mckenzie","Samy Wu Fung","Howard Heaton"],"abstract":"In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters $w$ are not directly observed; only contextual data $d$ that correlates with $w$ is available. It is tempting to use a neural network to predict $w$ given $d$. However, training such a model requires reconciling the discrete nature of combinatorial optimization with the gradient-based frameworks used to train neural networks. We study the case where the problem in question is an Integer Linear Program (ILP). We propose applying a three-operator splitting technique, also known as Davis-Yin splitting (DYS), to the quadratically regularized continuous relaxation of the ILP. We prove that the resulting scheme is compatible with the recently introduced Jacobian-free backpropagation (JFB). Our experiments on two representative ILPs: the shortest path problem and the knapsack problem, demonstrate that this combination-DYS on the forward pass, JFB on the backward pass-yields a scheme which scales more effectively to high-dimensional problems than existing schemes. All code associated with this paper is available at github.com/mines-opt-ml/fpo-dys.","url_abs":"https://arxiv.org/abs/2301.13395v4","url_pdf":"https://arxiv.org/pdf/2301.13395v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"faster-predict-and-optimize-with-three","repo_url":"https://github.com/mines-opt-ml/fpo-dys","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"faster-predict-and-optimize-with-three","repo_url":"https://github.com/mines-opt-ml/spo_with_dys","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2301.13395","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}