{"type":"ScholarlyArticle","title":"Contrastive Losses and Solution Caching for Predict-and-Optimize","authors":[{"name":"Maxime Mulamba","slug":"maxime-mulamba","given":"Maxime","family":"Mulamba","affiliation":"Data Analytics Laboratory , Vrije Universiteit Brussel , Belgium"},{"name":"Jayanta Mandi","slug":"jayanta-mandi","given":"Jayanta","family":"Mandi","affiliation":"Data Analytics Laboratory , Vrije Universiteit Brussel , Belgium"},{"name":"Michelangelo Diligenti","slug":"michelangelo-diligenti","given":"Michelangelo","family":"Diligenti","affiliation":"Department of Information Engineering and Mathematical Sciences , University of Siena , Italy"},{"name":"Michele Lombardi","slug":"michele-lombardi","given":"Michele","family":"Lombardi","affiliation":"Dipartimento di Informatica -Scienza e Ingegneria , University of Bologna , Italy"},{"name":"Victor Bucarey","slug":"victor-bucarey","given":"Victor","family":"Bucarey","affiliation":"Data Analytics Laboratory , Vrije Universiteit Brussel , Belgium"},{"name":"Tias Guns","slug":"tias-guns","given":"Tias","family":"Guns","affiliation":"Data Analytics Laboratory , Vrije Universiteit Brussel , Belgium; Department of Computer Science , KU Leuven , Belgium"}],"abstract":"Many decision-making processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. Recently, problems in this class have been successfully addressed via end-to-end learning approaches, which rely on solving one optimization problem for each training instance at every epoch. In this context, we provide two distinct contributions. First, we use a Noise Contrastive approach to motivate a family of surrogate loss functions, based on viewing non-optimal solutions as negative examples. Second, we address a major bottleneck of all predict-and-optimize approaches, i.e. the need to frequently recompute optimal solutions at training time. This is done via a solver-agnostic solution caching scheme, and by replacing optimization calls with a lookup in the solution cache. The method is formally based on an inner approximation of the feasible space and, combined with a cache lookup strategy, provides a controllable trade-off between training time and accuracy of the loss approximation. We empirically show that even a very slow growth rate is enough to match the quality of state-of-the-art methods, at a fraction of the computational cost.","doi":"10.24963/ijcai.2021/390","url":"https://ijcai.org/proceedings/2021/390","pdf":"https://ijcai.org/proceedings/2021/0390.pdf","markdown":"https://ijcai.org/proceedings/2021/390.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/390","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Machine Learning","track":"Main Track","number":390,"pages":{"first":2833,"last":2840},"keywords":["Machine Learning: Structured Prediction","Constraints and SAT: Constraint Optimization","Machine Learning: Neuro-Symbolic Methods"],"videos":[],"references":[{"position":1,"raw":"[Bach et al., 2017] Stephen H Bach, Matthias Broecheler, Bert Huang, and Lise Getoor. 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