Optimization Over Trained Neural Networks: Taking a Relaxing Walk

• URL: http://arxiv.org/abs/2401.03451v2
• Date: Sun, 28 Jan 2024 16:46:16 GMT
• Title: Optimization Over Trained Neural Networks: Taking a Relaxing Walk
• Authors: Jiatai Tong and Junyang Cai and Thiago Serra
• Abstract summary: We propose a more scalable solver based on exploring global and local linear relaxations of the neural network model. Our solver is competitive with a state-of-the-art MILP solver and the prior while producing better solutions with increases in input, depth, and number of neurons.
• Score: 4.517039147450688
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However, solving these formulations soon becomes difficult as the network size grows due to the weak linear relaxation and dense constraint matrix. We have seen improvements in recent years with cutting plane algorithms, reformulations, and an heuristic based on Mixed-Integer Linear Programming (MILP). In this work, we propose a more scalable heuristic based on exploring global and local linear relaxations of the neural network model. Our heuristic is competitive with a state-of-the-art MILP solver and the prior heuristic while producing better solutions with increases in input, depth, and number of neurons.

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