# Global Optimization Networks

arXiv: https://arxiv.org/abs/2202.01277 · HTML: https://mlsanity.com/paper/2202.01277/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 68 references that are in the map.
- First posted on arXiv 2 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Model Inversion Networks for Model-Based Optimization](https://mlsanity.com/paper/1912.13464/) (2019)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [RoMA: Robust Model Adaptation for Offline Model-based Optimization](https://mlsanity.com/paper/2110.14188/) (2021)
- [Monotonic Calibrated Interpolated Look-Up Tables](https://mlsanity.com/paper/1505.06378/) (2015)
- [Deontological Ethics By Monotonicity Shape Constraints](https://mlsanity.com/paper/2001.11990/) (2020)
- [Prediction Rule Reshaping](https://mlsanity.com/paper/1805.06439/) (2018)

## Built on by (most cited first, 2 of 2)

- [Asymmetric Certified Robustness via Feature-Convex Neural Networks](https://mlsanity.com/paper/2302.01961/) (2023)
- [Physics-Driven ML-Based Modelling for Correcting Inverse Estimation](https://mlsanity.com/paper/2309.13985/) (2023)

## Abstract (arXiv)

We consider the problem of estimating a good maximizer of a black-box function given noisy examples. To solve such problems, we propose to fit a new type of function which we call a global optimization network (GON), defined as any composition of an invertible function and a unimodal function, whose unique global maximizer can be inferred in O(D) time. In this paper, we show how to construct invertible and unimodal functions by using linear inequality constraints on lattice models. We also extend to conditional GONs that find a global maximizer conditioned on specified inputs of other dimensions. Experiments show the GON maximizers are statistically significantly better predictions than those produced by convex fits, GPR, or DNNs, and are more reasonable predictions for real-world problems.