Partition-based formulations for mixed-integer optimization of trained ReLU neural networks
This work addresses the problem of efficiently optimizing trained ReLU neural networks for researchers and practitioners in mixed-integer optimization.
This paper proposes mixed-integer formulations for trained ReLU neural networks by partitioning node inputs into groups and forming convex hulls over these partitions. This approach balances model size and tightness, outperforming existing formulations, particularly with strategies for partitioning variables.
This paper introduces a class of 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 partitions via disjunctive programming. At one extreme, one partition per input recovers the convex hull of a node, i.e., the tightest possible formulation for each node. For fewer partitions, we develop smaller relaxations that approximate the convex hull, and show that they outperform existing formulations. Specifically, we propose strategies for partitioning variables based on theoretical motivations and validate these strategies using extensive computational experiments. Furthermore, the proposed scheme complements known algorithmic approaches, e.g., optimization-based bound tightening captures dependencies within a partition.