# ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge

arXiv: https://arxiv.org/abs/2509.16300 · HTML: https://mlsanity.com/paper/2509.16300/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 71 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 30 of 42)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [BBDM: Image-to-image Translation with Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2205.07680/) (2022)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [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)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [ROBEL: Robotics Benchmarks for Learning with Low-Cost Robots](https://mlsanity.com/paper/1909.11639/) (2019)
- [Stochastic Zeroth-order Optimization in High Dimensions](https://mlsanity.com/paper/1710.10551/) (2017)
- [Autofocused oracles for model-based design](https://mlsanity.com/paper/2006.08052/) (2020)
- [Combining Latent Space and Structured Kernels for Bayesian Optimization over Combinatorial Spaces](https://mlsanity.com/paper/2111.01186/) (2021)
- [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)
- [Generative Pretraining for Black-Box Optimization](https://mlsanity.com/paper/2206.10786/) (2022)
- [Bidirectional Learning for Offline Infinite-width Model-based Optimization](https://mlsanity.com/paper/2209.07507/) (2022)
- [Data-Driven Offline Decision-Making via Invariant Representation Learning](https://mlsanity.com/paper/2211.11349/) (2022)
- [Importance-aware Co-teaching for Offline Model-based Optimization](https://mlsanity.com/paper/2309.11600/) (2023)
- [Parallel-mentoring for Offline Model-based Optimization](https://mlsanity.com/paper/2309.11592/) (2023)
- [Deep Learning in Protein Structural Modeling and Design](https://mlsanity.com/paper/2007.08383/) (2020)
- [Decentralized High-Dimensional Bayesian Optimization with Factor Graphs](https://mlsanity.com/paper/1711.07033/) (2017)
- [Bootstrapped Training of Score-Conditioned Generator for Offline Design of Biological Sequences](https://mlsanity.com/paper/2306.03111/) (2023)
- [ExPT: Synthetic Pretraining for Few-Shot Experimental Design](https://mlsanity.com/paper/2310.19961/) (2023)
- [Offline Model-Based Optimization via Policy-Guided Gradient Search](https://mlsanity.com/paper/2405.05349/) (2024)
- [Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization](https://mlsanity.com/paper/2407.01624/) (2024)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)

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

- [On the Learnability of Offline Model-Based Optimization: A Ranking Perspective](https://mlsanity.com/paper/2603.04000/) (2026)
- [Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization](https://mlsanity.com/paper/2605.11246/) (2026)
- [Black-Box Optimization From Small Offline Datasets via Meta Learning with Synthetic Tasks](https://mlsanity.com/paper/2604.12325/) (2026)
- [Rethinking Learnability in Offline Data-driven Optimization](https://mlsanity.com/paper/2609.01493/) (2026)

## Abstract (arXiv)

This paper studies the black-box optimization task which aims to find the maxima of a black-box function using a static set of its observed input-output pairs. This is often achieved via learning and optimizing a surrogate function with that offline data. Alternatively, it can also be framed as an inverse modeling task that maps a desired performance to potential input candidates that achieve it. Both approaches are constrained by the limited amount of offline data. To mitigate this limitation, we introduce a new perspective that casts offline optimization as a distributional translation task. This is formulated as learning a probabilistic bridge transforming an implicit distribution of low-value inputs (i.e., offline data) into another distribution of high-value inputs (i.e., solution candidates). Such probabilistic bridge can be learned using low- and high-value inputs sampled from synthetic functions that resemble the target function. These synthetic functions are constructed as the mean posterior of multiple Gaussian processes fitted with different parameterizations on the offline data, alleviating the data bottleneck. The proposed approach is evaluated on an extensive benchmark comprising most recent methods, demonstrating significant improvement and establishing a new state-of-the-art performance. Our code is publicly available at https://github.com/cuong-dm/ROOT.