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A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences
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Surveys high-dimensional Bayesian optimization methods for discrete sequences and benchmarks ~15 solvers on Ehrlich sequence-design functions and PMO latent-space molecule tasks, releasing the poli and poli-baselines software.
Problem
Published high-dimensional Bayesian optimization (HDBO) methods for discrete sequences use heterogeneous experimental setups and are hard to replicate or apply to real-world problems with sequence lengths around 10^2 and larger alphabets.
Approach
A seven-family taxonomy of HDBO methods, plus a unified framework (poli, poli-baselines) that isolates black boxes and solvers in separate environments and standardizes initialization, budgets, and logging for benchmarking on Ehrlich functions and PMO.
Key results
- On Ehrlich functions, Bounce solves PestControlEquiv in all 5 replications (1.000) and DirectedEvolution reaches 1.000 on Ehrlich L=5, with BO methods often matching or underperforming greedy baselines on harder tasks.
- On PMO with a 128-dim latent space, CMA-ES has the highest normalized sum (21.15) while Bounce (1.59) and ProbRep (3.95) perform worst; latent-space optimizers beat discrete-space ones.
- On PMO with a 2-dim latent space, Hvarfner's VanillaBO and Random LineBO reach 19.54 normalized sum, while Bounce scores 1.65.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use optimizers operating on learned latent representations rather than directly on discrete sequence space | PMO small-molecule optimization · PMO | average best result | Helped |
| Increase sequence complexity (longer sequence or larger problem) | Bayesian optimization and sequence-space optimizers · Ehrlich sequence design | average best value | Hurt |
| Use simpler baselines instead of most BO methods at low budgets | Small-molecule optimization · PMO | optimization performance | Helped |
| Optimize in 2D latent space rather than 128D latent space | PMO optimizers · PMO | normalized sum: 19.54 vs 21.15 | Mixed |
Surprising findings
- For low budgets, simple baselines such as DirectedEvolution and HillClimbing perform as well as or better than most BO methods.
- Discrete-space optimizers (Bounce, ProbRep) perform poorly on PMO compared to latent-space methods.
Limitations
- Only a subset of the surveyed HDBO methods were benchmarked.
- Black boxes are often simple closed-form or data-driven oracles, limiting real-world relevance.
- No systematic analysis of design choices across optimization campaigns.
Experimental setup
Datasets: Zinc250k Ehrlich functions PMO benchmark
Benchmarks: Ehrlich functions (PestControlEquiv, Ehrlich L=5/15/64) PMO
Metrics: average best objective value normalized sum across oracles
Baselines: VanillaBO RandomLineBO Turbo BAxUS SAASBO Bounce ProbRep DirectedEvolution HillClimbing GeneticAlgorithm CMA-ES
Builds on: TuRBO BoTorch GPyTorch Ehrlich functions PMO benchmark
Closest papers by meaning
- Unifying Likelihood-free Inference with Black-box Optimization and Beyond (ICLR 2022 · similarity 0.89)
- Approximation-Aware Bayesian Optimization (NeurIPS 2024 · similarity 0.89)
- Understanding High-Dimensional Bayesian Optimization (ICML 2025 · similarity 0.88)
- Empower Structure-Based Molecule Optimization with Gradient Guided Bayesian Flow Networks (ICML 2025 · similarity 0.88)
- Optimistic Games for Combinatorial Bayesian Optimization with Application to Protein Design (ICLR 2025 · similarity 0.87)
- Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization (ICML 2025 · similarity 0.87)
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