Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks

TL;DR

This paper investigates the balance between the tightness of activation bounds and computational effort in MILP models of ReLU neural networks, providing practical guidelines for their implementation.

Contribution

It analyzes the tradeoffs in bound tightening for MILP models of ReLU networks and offers guidelines considering network structure, regularization, and rounding effects.

Findings

Tighter bounds improve MILP model accuracy but increase computational cost.

Network structure and regularization influence the effectiveness of bound tightening.

Guidelines help optimize the tradeoff between bound tightness and computational effort.

Abstract

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.