# Parameterized Convex Universal Approximators for Decision-Making Problems

arXiv: https://arxiv.org/abs/2201.06298 · HTML: https://mlsanity.com/paper/2201.06298/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 17 Jan 2022.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [Convex Optimization in Julia](https://mlsanity.com/paper/1410.4821/) (2014)
- [A Universal Approximation Result for Difference of log-sum-exp Neural Networks](https://mlsanity.com/paper/1905.08503/) (2019)
- [Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding](https://mlsanity.com/paper/1312.3039/) (2013)

## Built on by (most cited first, 4 of 4)

- [Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference](https://mlsanity.com/paper/2310.16975/) (2023)
- [Asymmetric Certified Robustness via Feature-Convex Neural Networks](https://mlsanity.com/paper/2302.01961/) (2023)
- [Parameterized Convex Minorant for Objective Function Approximation in Amortized Optimization](https://mlsanity.com/paper/2310.02519/) (2023)
- [Universal Representation of Generalized Convex Functions and their Gradients](https://mlsanity.com/paper/2509.04477/) (2025)

## Abstract (arXiv)

Parameterized max-affine (PMA) and parameterized log-sum-exp (PLSE) networks are proposed for general decision-making problems. The proposed approximators generalize existing convex approximators, namely, max-affine (MA) and log-sum-exp (LSE) networks, by considering function arguments of condition and decision variables and replacing the network parameters of MA and LSE networks with continuous functions with respect to the condition variable. The universal approximation theorem of PMA and PLSE is proven, which implies that PMA and PLSE are shape-preserving universal approximators for parameterized convex continuous functions. Practical guidelines for incorporating deep neural networks within PMA and PLSE networks are provided. A numerical simulation is performed to demonstrate the performance of the proposed approximators. The simulation results support that PLSE outperforms other existing approximators in terms of minimizer and optimal value errors with scalable and efficient computation for high-dimensional cases.