  Deep neural networks have become an important tool for use in actuarial
tasks, due to the significant gains in accuracy provided by these techniques
compared to traditional methods, but also due to the close connection of these
models to the Generalized Linear Models (GLMs) currently used in industry.
Whereas constraining GLM parameters relating to insurance risk factors to be
smooth or exhibit monotonicity is trivial, methods to incorporate such
constraints into deep neural networks have not yet been developed. This is a
barrier for the adoption of neural networks in insurance practice since
actuaries often impose these constraints for commercial or statistical reasons.
In this work, we present a novel method for enforcing constraints within deep
neural network models, and we show how these models can be trained. Moreover,
we provide example applications using real-world datasets. We call our proposed
method ICEnet to emphasize the close link of our proposal to the individual
conditional expectation (ICE) model interpretability technique.
