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Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization
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Proposes DiBO, which iterates training a diffusion prior plus proxy ensemble and sampling candidates from a posterior (prior times exp(beta*UCB)) fine-tuned with relative trajectory balance, followed by local search and filtering, for high-dimensional black-box optimization.
Problem
Sample-efficient optimization of high-dimensional black-box functions where BO struggles with acquisition maximization and uncertainty estimation, and prior generative-model methods have limited expressivity.
Approach
Cast candidate selection as posterior inference: multiply a diffusion prior by an exponentiated UCB score from a deep ensemble, and amortize sampling by fine-tuning the diffusion model with relative trajectory balance (off-policy with a replay buffer), then refine samples via PF-ODE-based local search and top-B filtering on the unnormalized posterior.
Key results
- On synthetic 200D and 400D functions (Rastrigin, Ackley, Levy, Rosenbrock), DiBO significantly outperforms all listed BO, evolutionary, and generative baselines according to the authors.
- On real-world tasks (HalfCheetah-102D, RoverPlanning-100D, DNA-180D), DiBO consistently surpasses baselines in both performance and sample efficiency.
- Removing reweighted training, local search, or filtering significantly degrades performance; per-round running time of DiBO is comparable to generative baselines and mostly faster than BO methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DiBO instead of the evaluated baselines | high-dimensional synthetic optimization · Rastrigin, Ackley, Levy, and Rosenbrock, 200D and 400D | optimization performance | Helped |
| use DiBO instead of the evaluated baselines | high-dimensional black-box optimization · HalfCheetah-102D, RoverPlanning-100D, and DNA-180D | performance and sample efficiency | Helped |
| add reweighted training focused on high-scoring data (ablation) | DiBO · Rastrigin-200D and HalfCheetah-102D | optimization performance | Helped |
| add local search and filtering (ablation) | DiBO · Rastrigin-200D and HalfCheetah-102D | sample efficiency | Helped |
| add amortized posterior inference instead of proposing directly from the diffusion prior (ablation) | DiBO · Rastrigin-200D and HalfCheetah-102D | optimization performance | Helped |
| increase training epochs (ablation) | DiBO · Rastrigin-200D and HalfCheetah-102D | optimization performance | Mixed |
| increase local search steps too much (ablation) | DiBO · Rastrigin-200D and HalfCheetah-102D | optimization performance | Hurt |
| add off-policy training to amortized inference (ablation) | DiBO · Rastrigin-200D and HalfCheetah-102D | optimization performance | Helped |
| use a large batch size (ablation) | DiBO · synthetic functions | convergence speed | Hurt |
| use a small buffer size (ablation) | DiBO · optimization tasks | optimization performance | Hurt |
| use only on-policy training instead of off-policy training (ablation) | DiBO amortized inference · Rastrigin-200D and HalfCheetah-102D | optimization performance | Hurt |
| use an ensemble of proxies for uncertainty estimation instead of MC dropout or one proxy (ablation) | DiBO · HalfCheetah-102D | sample efficiency | Helped |
Surprising findings
- Naively increasing the number of training epochs does not improve performance and can cause overfitting of proxy and diffusion models.
- Generative model baselines such as CbAS and MINs perform well early but stall, while BO methods are competitive yet less sample-efficient than DiBO.
Limitations
- The diffusion model must be retrained from scratch on the updated dataset every round, which is costly.
- Larger local search steps and buffer sizes improve results but raise computational complexity.
Experimental setup
Datasets: Rastrigin Ackley Levy Rosenbrock HalfCheetah-102D RoverPlanning-100D LassoBench DNA-180D
Benchmarks: Rastrigin Ackley Levy Rosenbrock HalfCheetah-102D RoverPlanning-100D LassoBench DNA-180D
Metrics: best objective value vs evaluations running time per round
Baselines: TuRBO LA-MCTS MCMC-BO CMA-BO CMA-ES CbAS MINs DDOM Diff-BBO
Builds on: relative trajectory balance denoising diffusion probabilistic models DDOM Diff-BBO
Closest papers by meaning
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