Certified Monotonic Neural Networks

TL;DR

This paper introduces a novel approach to certify the monotonicity of general piece-wise linear neural networks using mixed integer linear programming, enabling flexible, accurate, and provably monotonic models without restrictive design constraints.

Contribution

It proposes a general certification method for neural networks' monotonicity that does not rely on specific model structures or constraints, improving flexibility and accuracy.

Findings

Outperforms state-of-the-art methods like Deep Lattice Networks

Enables training of neural networks with certifiable monotonicity

Provides a flexible approach applicable to arbitrary model structures

Abstract

Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks either require specifically designed model structures to ensure monotonicity, which can be too restrictive/complicated, or enforce monotonicity by adjusting the learning process, which cannot provably guarantee the learned model is monotonic on selected features. In this work, we propose to certify the monotonicity of the general piece-wise linear neural networks by solving a mixed integer linear programming problem.This provides a new general approach for learning monotonic neural networks with arbitrary model structures. Our method allows us to train neural networks with heuristic monotonicity regularizations, and we can gradually increase the regularization magnitude until the learned network is certified monotonic. Compared to prior works, our approach does not require human-designed constraints on the weight space and also yields more accurate approximation. Empirical studies on various datasets demonstrate the efficiency of our approach over the state-of-the-art methods, such as Deep Lattice Networks.