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Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks
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The use of Mixed-Integer Linear Programming (MILP) models to represent neural networks with Rectified Linear Unit (ReLU) activations has become increasingly widespread in the last decade. This has enabled the use of MILP technology to test-or stress-their behavior, to adversarially improve their training, and to embed them in optimization models leveraging their predictive power. Many of these MILP models rely on activation bounds. That is, bounds on the input values of each neuron. In this work, we explore the tradeoff between the tightness of these bounds and the computational effort of solving the resulting MILP models. We provide guidelines for implementing these models based on the impact of network structure, regularization, and rounding.
Forward citations
Cited by 2 Pith papers
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Contextual Stochastic Optimization with Decision-Dependent Uncertainty via Nonparametric Learning
ER-DD-SAA with exact MIP embeddings of kNN/CART/ReLU NNs is consistent and asymptotically optimal, and BD-CG solves the kNN two-stage case to global optimality in finite iterations.
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An analysis of optimization problems involving ReLU neural networks
L1 regularization of ReLU network weights is the most effective lever for speeding up mixed-integer optimization over the network, and there is a quantified trade-off between model redundancy and solver runtime.
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