# Conservative quantum offline model-based optimization

arXiv: https://arxiv.org/abs/2506.19714 · HTML: https://mlsanity.com/paper/2506.19714/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 24 Jun 2025.

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

- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Model Inversion Networks for Model-Based Optimization](https://mlsanity.com/paper/1912.13464/) (2019)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [RoMA: Robust Model Adaptation for Offline Model-based Optimization](https://mlsanity.com/paper/2110.14188/) (2021)
- [Data-Driven Offline Decision-Making via Invariant Representation Learning](https://mlsanity.com/paper/2211.11349/) (2022)
- [An Introduction to Quantum Machine Learning for Engineers](https://mlsanity.com/paper/2205.09510/) (2022)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Functional Graphical Models: Structure Enables Offline Data-Driven Optimization](https://mlsanity.com/paper/2401.05442/) (2024)
- [Incorporating Surrogate Gradient Norm to Improve Offline Optimization Techniques](https://mlsanity.com/paper/2503.04242/) (2025)
- [Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problems](https://mlsanity.com/paper/2203.10215/) (2022)
- [Quantum Extremal Learning](https://mlsanity.com/paper/2205.02807/) (2022)

## Abstract (arXiv)

Offline model-based optimization (MBO) refers to the task of optimizing a black-box objective function using only a fixed set of prior input-output data, without any active experimentation. Recent work has introduced quantum extremal learning (QEL), which leverages the expressive power of variational quantum circuits to learn accurate surrogate functions by training on a few data points. However, as widely studied in the classical machine learning literature, predictive models may incorrectly extrapolate objective values in unexplored regions, leading to the selection of overly optimistic solutions. In this paper, we propose integrating QEL with conservative objective models (COM) - a regularization technique aimed at ensuring cautious predictions on out-of-distribution inputs. The resulting hybrid algorithm, COM-QEL, builds on the expressive power of quantum neural networks while safeguarding generalization via conservative modeling. Empirical results on benchmark optimization tasks demonstrate that COM-QEL reliably finds solutions with higher true objective values compared to the original QEL, validating its superiority for offline design problems.