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ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge
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Casts offline black-box optimization as distributional translation: a Brownian-bridge diffusion model is trained on low-to-high-value pairs drawn from GP posterior-mean synthetic functions and applied to top offline designs to generate better candidates.
Problem
Offline black-box optimization must find high-value designs from a static dataset, but surrogate and inverse models are limited by scarce high-value examples and erratic out-of-distribution predictions.
Approach
Frame offline optimization as learning a probabilistic bridge (Brownian bridge diffusion) that transports low-value offline inputs to high-value candidates, with training pairs sampled from gradient descent/ascent on the posterior means of multiple GPs fitted with different hyperparameters to the offline data.
Key results
- ROOT achieves mean rank 1.25 of 22 methods on Design-Bench 100th percentile, with 0.972 on D'Kitty and 0.986 on TFBind8 (new SOTA on 3 of 4 Design-Bench tasks).
- On RNA-Binding tasks ROOT ranks first on all three, e.g., 0.956 on RNA-A vs 0.913 for Boot-Gen.
- At the 100th percentile on Ant, CMA-ES scores higher (1.561 ± 0.896) than ROOT (0.965 ± 0.014), with ROOT having far lower variance.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use probabilistic-bridge learning instead of gradient ascent on the GP posterior mean (ablation) | ROOT · Design-Bench tasks | score | Helped |
| initialize from the highest-scoring offline points rather than random points (ablation) | ROOT · Ant Morphology | score: 0.953 ± 0.014 -> 0.965 ± 0.014 | Helped |
| initialize from the highest-scoring offline points rather than the lowest-scoring offline points (ablation) | ROOT · Ant Morphology | score: 0.545 ± 0.214 -> 0.965 ± 0.014 | Helped |
| increase synthetic-data gradient steps from M=25 to M=100 (ablation) | ROOT · TFBind8 | score: 0.952 ± 0.024 -> 0.986 ± 0.007 | Helped |
| increase synthetic-data gradient steps from M=25 to M=100 (ablation) | ROOT · TFBind10 | score: 0.640 ± 0.039 -> 0.685 ± 0.053 | Helped |
| increase synthetic-data gradient steps from M=25 to M=100 (ablation) | ROOT · Ant Morphology | score: 0.968 ± 0.009 -> 0.965 ± 0.014 | Mixed |
| increase synthetic-data gradient steps from M=25 to M=100 (ablation) | ROOT · D'Kitty Morphology | score: 0.972 ± 0.003 -> 0.972 ± 0.005 | No clear effect |
| use ROOT instead of ExPT in the few-shot setting | offline optimization · Ant Morphology | score: 0.940 ± 0.027 -> 0.942 ± 0.035 | Helped |
| use ROOT instead of ExPT in the few-shot setting | offline optimization · TFBind8 | score: 0.874 ± 0.071 -> 0.895 ± 0.086 | Helped |
Surprising findings
- CMA-ES achieves the highest single-design maximum on Ant but collapses near zero at the 80th and 50th percentiles, indicating only one good design per run.
Limitations
- Performance depends on the number of gradient steps M and hyperparameters of GP synthetic function generation (ℓ0, σ0², δ, step size), which are set per task type.
- On Ant at the 100th percentile, CMA-ES outperforms ROOT in mean score, and ROOT does not win every percentile/task (e.g., TFBind10 at the 80th percentile is competitive rather than best).
Experimental setup
Datasets: Design-Bench (Ant Morphology, D'Kitty Morphology, TF-Bind-8, TF-Bind-10) RNA-Binding (ViennaRNA) tasks RNA-A, RNA-B, RNA-C
Benchmarks: Design-Bench (Ant, D'Kitty, TFBind8, TFBind10) RNA-Binding (RNA-A, RNA-B, RNA-C)
Metrics: maximum score among 128 candidates (100th percentile) 80th and 50th percentile scores mean rank
Baselines: BO-qEI CMA-ES REINFORCE COMs CbAS MINs RoMA DDOM ICT Tri-mentoring GTG BDI
Builds on: denoising diffusion probabilistic model Brownian bridge diffusion model classifier-free guidance Gaussian processes
Closest papers by meaning
- Learning Surrogates for Offline Black-Box Optimization via Gradient Matching (ICML 2024 · similarity 0.90)
- Incorporating Surrogate Gradient Norm to Improve Offline Optimization Techniques (NeurIPS 2024 · similarity 0.89)
- Offline Model-Based Optimization via Policy-Guided Gradient Search (AAAI 2024 · similarity 0.88)
- Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization (NeurIPS 2024 · similarity 0.88)
- Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization (NeurIPS 2026 · similarity 0.88)
- Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization (ICML 2025 · similarity 0.87)
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