# Generative Pretraining for Black-Box Optimization

arXiv: https://arxiv.org/abs/2206.10786 · HTML: https://mlsanity.com/paper/2206.10786/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 60 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Online Decision Transformer](https://mlsanity.com/paper/2202.05607/) (2022)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [Reinforcement Learning Upside Down: Don't Predict Rewards -- Just Map Them to Actions](https://mlsanity.com/paper/1912.02875/) (2019)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [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)
- [ROBEL: Robotics Benchmarks for Learning with Low-Cost Robots](https://mlsanity.com/paper/1909.11639/) (2019)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Sequential Neural Processes](https://mlsanity.com/paper/1906.10264/) (2019)
- [Autofocused oracles for model-based design](https://mlsanity.com/paper/2006.08052/) (2020)
- [On Explore-Then-Commit Strategies](https://mlsanity.com/paper/1605.08988/) (2016)
- [RoMA: Robust Model Adaptation for Offline Model-based Optimization](https://mlsanity.com/paper/2110.14188/) (2021)
- [Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation](https://mlsanity.com/paper/2102.07970/) (2021)
- [Best arm identification in multi-armed bandits with delayed feedback](https://mlsanity.com/paper/1803.10937/) (2018)
- [Knowing The What But Not The Where in Bayesian Optimization](https://mlsanity.com/paper/1905.02685/) (2019)
- [JUMBO: Scalable Multi-task Bayesian Optimization using Offline Data](https://mlsanity.com/paper/2106.00942/) (2021)

## Built on by (most cited first, 30 of 36)

- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [Masked Autoencoding for Scalable and Generalizable Decision Making](https://mlsanity.com/paper/2211.12740/) (2022)
- [LICO: Large Language Models for In-Context Molecular Optimization](https://mlsanity.com/paper/2406.18851/) (2024)
- [ExPT: Synthetic Pretraining for Few-Shot Experimental Design](https://mlsanity.com/paper/2310.19961/) (2023)
- [Position: Leverage Foundational Models for Black-Box Optimization](https://mlsanity.com/paper/2405.03547/) (2024)
- [Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization](https://mlsanity.com/paper/2407.01624/) (2024)
- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Reinforced In-Context Black-Box Optimization](https://mlsanity.com/paper/2402.17423/) (2024)
- [Pretrained Optimization Model for Zero-Shot Black Box Optimization](https://mlsanity.com/paper/2405.03728/) (2024)
- [Offline Model-Based Optimization by Learning to Rank](https://mlsanity.com/paper/2410.11502/) (2024)
- [Preference-Guided Diffusion for Multi-Objective Offline Optimization](https://mlsanity.com/paper/2503.17299/) (2025)
- [Generative Adversarial Model-Based Optimization via Source Critic Regularization](https://mlsanity.com/paper/2402.06532/) (2024)
- [Design Editing for Offline Model-based Optimization](https://mlsanity.com/paper/2405.13964/) (2024)
- [Decision Stacks: Flexible Reinforcement Learning via Modular Generative Models](https://mlsanity.com/paper/2306.06253/) (2023)
- ["Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood](https://mlsanity.com/paper/2405.16730/) (2024)
- [Robust Guided Diffusion for Offline Black-Box Optimization](https://mlsanity.com/paper/2410.00983/) (2024)
- [Towards Universal Offline Black-Box Optimization via Learning Language Model Embeddings](https://mlsanity.com/paper/2506.07109/) (2025)
- [Reliable Conditioning of Behavioral Cloning for Offline Reinforcement Learning](https://mlsanity.com/paper/2210.05158/) (2022)
- [Boosting Offline Optimizers with Surrogate Sensitivity](https://mlsanity.com/paper/2503.04181/) (2025)
- [Incorporating Surrogate Gradient Norm to Improve Offline Optimization Techniques](https://mlsanity.com/paper/2503.04242/) (2025)
- [ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge](https://mlsanity.com/paper/2509.16300/) (2025)
- [Robust Adaptation of Foundation Models with Black-Box Visual Prompting](https://mlsanity.com/paper/2407.17491/) (2024)
- [Cliqueformer: Model-Based Optimization with Structured Transformers](https://mlsanity.com/paper/2410.13106/) (2024)
- [Diffusion Large Language Models for Black-Box Optimization](https://mlsanity.com/paper/2601.14446/) (2026)
- [ROMO: Retrieval-enhanced Offline Model-based Optimization](https://mlsanity.com/paper/2310.07560/) (2023)
- [From Function to Distribution Modeling: A PAC-Generative Approach to Offline Optimization](https://mlsanity.com/paper/2401.02019/) (2024)
- [Learning Design-Score Manifold to Guide Diffusion Models for Offline Optimization](https://mlsanity.com/paper/2506.05680/) (2025)
- [ZeroShotOpt: Towards Zero-Shot Pretrained Models for Efficient Black-Box Optimization](https://mlsanity.com/paper/2510.03051/) (2025)
- [Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization](https://mlsanity.com/paper/2605.11246/) (2026)

## Abstract (arXiv)

Many problems in science and engineering involve optimizing an expensive black-box function over a high-dimensional space. For such black-box optimization (BBO) problems, we typically assume a small budget for online function evaluations, but also often have access to a fixed, offline dataset for pretraining. Prior approaches seek to utilize the offline data to approximate the function or its inverse but are not sufficiently accurate far from the data distribution. We propose BONET, a generative framework for pretraining a novel black-box optimizer using offline datasets. In BONET, we train an autoregressive model on fixed-length trajectories derived from an offline dataset. We design a sampling strategy to synthesize trajectories from offline data using a simple heuristic of rolling out monotonic transitions from low-fidelity to high-fidelity samples. Empirically, we instantiate BONET using a causally masked Transformer and evaluate it on Design-Bench, where we rank the best on average, outperforming state-of-the-art baselines.