BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ruth Misener (Imperial College London) DTSTART:20210618T130000Z DTEND:20210618T140000Z DTSTAMP:20260423T003244Z UID:MPML/47 DESCRIPTION:Title: Pa rtition-based formulations for mixed-integer optimization of trained ReLU neural networks\nby Ruth Misener (Imperial College London) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nT his work develops a class of relaxations in between the big-M and convex h ull formulations of disjunctions\, drawing advantages from both. We show t hat this class leads to mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the p artitions via disjunctive programming. At one extreme\, one partition per input recovers the convex hull of a node\, i.e.\, the tightest possible fo rmulation for each node. For fewer partitions\, we develop smaller relaxat ions that approximate the convex hull\, and show that they outperform exis ting formulations. Specifically\, we propose strategies for partitioning v ariables based on theoretical motivations and validate these strategies us ing extensive computational experiments. Furthermore\, the proposed scheme complements known algorithmic approaches\, e.g.\, optimization-based boun d tightening captures dependencies within a partition.\n\nThis joint work with Calvin Tsay\, Jan Kronqvist\, Alexander Thebelt is based on two paper s: https://arxiv.org/abs/2102.04373 & https://arxiv.org/abs/2101.12708\n LOCATION:https://researchseminars.org/talk/MPML/47/ END:VEVENT END:VCALENDAR