Constraint Guided Gradient Descent: Guided Training with Inequality Constraints

TL;DR

This paper introduces the Constraint Guided Gradient Descent (CGGD) framework, which incorporates domain knowledge as inequality constraints into neural network training, ensuring models satisfy these constraints without complex transformations.

Contribution

The proposed CGGD method allows direct integration of inequality constraints into training, guaranteeing constraint satisfaction and reducing dependence on initialization, unlike prior neuro-symbolic approaches.

Findings

CGGD ensures models satisfy inequality constraints on training data.

Training with CGGD is less sensitive to initial network parameters.

Empirical results show improved constraint satisfaction across datasets.

Abstract

Deep learning is typically performed by learning a neural network solely from data in the form of input-output pairs ignoring available domain knowledge. In this work, the Constraint Guided Gradient Descent (CGGD) framework is proposed that enables the injection of domain knowledge into the training procedure. The domain knowledge is assumed to be described as a conjunction of hard inequality constraints which appears to be a natural choice for several applications. Compared to other neuro-symbolic approaches, the proposed method converges to a model that satisfies any inequality constraint on the training data and does not require to first transform the constraints into some ad-hoc term that is added to the learning (optimisation) objective. Under certain conditions, it is shown that CGGD can converges to a model that satisfies the constraints on the training set, while prior work does not necessarily converge to such a model. It is empirically shown on two independent and small data sets that CGGD makes training less dependent on the initialisation of the network and improves the constraint satisfiability on all data.