# Functional Graphical Models: Structure Enables Offline Data-Driven Optimization

arXiv: https://arxiv.org/abs/2401.05442 · HTML: https://mlsanity.com/paper/2401.05442/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 53 references that are in the map.
- First posted on arXiv 8 Jan 2024.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [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)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?](https://mlsanity.com/paper/2301.12844/) (2023)
- [ConfuciuX: Autonomous Hardware Resource Assignment for DNN Accelerators using Reinforcement Learning](https://mlsanity.com/paper/2009.02010/) (2020)
- [Data-Driven Offline Decision-Making via Invariant Representation Learning](https://mlsanity.com/paper/2211.11349/) (2022)
- [Data-Driven Offline Optimization For Architecting Hardware Accelerators](https://mlsanity.com/paper/2110.11346/) (2021)
- [Decentralized High-Dimensional Bayesian Optimization with Factor Graphs](https://mlsanity.com/paper/1711.07033/) (2017)

## Built on by (most cited first, 11 of 11)

- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Offline Model-Based Optimization by Learning to Rank](https://mlsanity.com/paper/2410.11502/) (2024)
- [Monotone, Bi-Lipschitz, and Polyak-Lojasiewicz Networks](https://mlsanity.com/paper/2402.01344/) (2024)
- [Towards Universal Offline Black-Box Optimization via Learning Language Model Embeddings](https://mlsanity.com/paper/2506.07109/) (2025)
- [Cliqueformer: Model-Based Optimization with Structured Transformers](https://mlsanity.com/paper/2410.13106/) (2024)
- [On the Learnability of Offline Model-Based Optimization: A Ranking Perspective](https://mlsanity.com/paper/2603.04000/) (2026)
- [Learning Design-Score Manifold to Guide Diffusion Models for Offline Optimization](https://mlsanity.com/paper/2506.05680/) (2025)
- [Conservative quantum offline model-based optimization](https://mlsanity.com/paper/2506.19714/) (2025)
- [Leveraging Discrete Function Decomposability for Scientific Design](https://mlsanity.com/paper/2511.03032/) (2025)
- [Offline Materials Optimization with CliqueFlowmer](https://mlsanity.com/paper/2603.06082/) (2026)
- [Rethinking Learnability in Offline Data-driven Optimization](https://mlsanity.com/paper/2609.01493/) (2026)

## Abstract (arXiv)

While machine learning models are typically trained to solve prediction problems, we might often want to use them for optimization problems. For example, given a dataset of proteins and their corresponding fluorescence levels, we might want to optimize for a new protein with the highest possible fluorescence. This kind of data-driven optimization (DDO) presents a range of challenges beyond those in standard prediction problems, since we need models that successfully predict the performance of new designs that are better than the best designs seen in the training set. It is not clear theoretically when existing approaches can even perform better than the naive approach that simply selects the best design in the dataset. In this paper, we study how structure can enable sample-efficient data-driven optimization. To formalize the notion of structure, we introduce functional graphical models (FGMs) and show theoretically how they can provide for principled data-driven optimization by decomposing the original high-dimensional optimization problem into smaller sub-problems. This allows us to derive much more practical regret bounds for DDO, and the result implies that DDO with FGMs can achieve nearly optimal designs in situations where naive approaches fail due to insufficient coverage of the offline data. We further present a data-driven optimization algorithm that inferes the FGM structure itself, either over the original input variables or a latent variable representation of the inputs.