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Department of Mechanical Engineering
IEEE OJ-CSYS

Paper in IEEE OJ-CSYS

© RCS ​/​ DT
Dieter Teichrib and Moritz Schulze Darup published the paper “On the Representation of Piecewise Quadratic Functions by Neural Networks” in the special section Intersection of Machine Learning with Control of the IEEE Open Journal of Control Systems.

Effectively approximating piecewise quadratic (PWQ) functions is crucial for a successful application of many reinforcement learning methods, such as Q-learning, for various applications. In this paper, we present the first neural networks that provably allow an exact representation of continuous PWQ functions with polyhedral domain partitions and validate experimentally that these neural networks (NN) lead to approximations with significantly lower approximation errors compared to classical NNs. 

The derived NNs build on a new decomposition of PWQ functions into a convex piecewise affine part and a special remaining PWQ part , where both parts are such that they can be represented by maxout neurons as illustrated in the figure. The augmented input vector xi contains all quadratic monomials of x. Contact Dieter for further details or have a look at the paper:

D. Teichrib and M. Schulze Darup, On the Representation of Piecewise Quadratic Functions by Neural Networks, in IEEE Open Journal of Control Systems, 2025, DOI: 10.1109/OJCSYS.2025.3607844