Feedforward networks with monotone constraints

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Sample-Efficient Reinforcement Learning via Counterfactual-Based Data Augmentation (2020, background): “In experiments, this strict monotonicity can be easily implemented through monotonic multi-layer perceptron network [21], in which positive signs of the weights are guaranteed by introducing their exponential form [22].”
Monotonic Multi-layer Perceptron Networks as Universal Approximators (2005, background): “The monotonic multi-layer perceptron network (MONMLP) which is presented here is an approach for multi-dimensional function approximation ensuring monotonicity for selected input-output relations [6] [7](1).”
Neural Networks in R Using the Stuttgart Neural Network Simulator: RSNNS (2012, methodology): “…version of the algorithm” presented by Anastasiadis et al. (2005), and a method for “the calculation of generalized weights”, which are not present in SNNS . monmlp The package monmlp (Cannon 2011a) implements a multi-layer perceptron with partial monotonicity constraints (Zhang and Zhang 1999).”