BBO-Pile

BBO-Pile is the first large-scale, open-source dataset of black-box optimization (BBO) trajectories, built to pre-train foundation models that imitate optimization behaviour across diverse problem classes. It contains 557,100 completed optimization runs collected over 3,095 distinct black-box tasks, spanning hyperparameter optimization, neural architecture search, and synthetic global-optimization problems. It accompanies the paper An Open-Source Training Dataset for Foundation Models for Black-box Optimization (arXiv:2605.23417).

Motivation

Most black-box optimizers require extensive per-problem tuning, which limits how well they generalize across domains. Foundation models that learn optimization principles from a large collection of trajectories are a promising alternative, but prior efforts relied on non-public datasets or purely synthetic data, hurting reproducibility and transfer to real problems. BBO-Pile addresses this gap by releasing a large, diverse, real-world corpus of optimization trajectories under an open license.

Dataset Composition

Trajectories were generated by running 6 optimizers — five state-of-the-art algorithms plus random search as a baseline — across a broad collection of benchmark families. Because evaluating real black-box problems at this scale would be prohibitively expensive, trajectories are collected against offline surrogate / tabular benchmarks rather than live objectives. A simple k-nearest-neighbor regressor is used as the surrogate across all benchmarks to minimize additional modeling bias.

Benchmark families

Category	Benchmark families
Hyperparameter optimization	HPO-B, LC-Bench, PD1, TabRepo
Neural architecture search	FC-Net, NAS-Bench-201
Masked variants	masked FC-Net, masked NAS-Bench-201
Synthetic	28 synthetic global-optimization problems

The masked families are derived by masking up to two hyperparameters across all permutations within a search space; masked hyperparameters are fixed to their marginal best value (the setting yielding the best mean performance when marginalizing over the remaining dimensions). This expands both the number and diversity of tasks.

Total optimization runs	557,100
Distinct black-box tasks	3,095
Optimizers	6 (5 state-of-the-art + random search)

Data Format

Each record is an optimization trajectory (x_t, y_t) for t = 1..T, where x_t is an input configuration in a D-dimensional search space and y_t is the observed objective value at step t. Trajectories are encoded and tokenized following the OptFormer-style scheme of Chen et al. Metadata — the optimizer name and a per-dimension description of the search space (type, bounds, scale) — is serialized first, followed by the sequence of evaluated configurations and their outcomes. An illustrative encoding:

<algorithm>:RS
<type>:<UNI>,<min_value>:0.01,<max_value>:1.0,<log-scale>&
<type>:<INT>,<min_value>:1,<max_value>:5,<linear-scale>&
<type>:<CATEGORICAL>,<categories>:[0, 1]
120,200,<1>*300|60,50,<0>*200|

This string representation lets a single decoder-only transformer model heterogeneous search spaces (continuous, integer, categorical; linear or log scale) with one vocabulary.

Intended Use

BBO-Pile is designed for pre-training foundation models for black-box optimization. In the accompanying paper it is used to train a family of decoder-only transformers ranging from 2M to 80M parameters and 200M to 2B training tokens, and to study their scaling behaviour with respect to compute. Results indicate that large-scale pre-training is a viable and effective way to imitate black-box optimizers. Other suitable uses include meta-learning and transfer-learning research, algorithm-behaviour analysis, benchmarking learned optimizers, and studying scaling laws for optimization models.

Usage

from datasets import load_dataset
ds = load_dataset("bbo-pile/bbo-pile", split="train")
print(ds[0])

Limitations and Considerations

• Surrogate objectives. Objective values come from offline tabular lookups or k-NN surrogates, not live evaluations, so they approximate the true response surfaces of the underlying benchmarks.
• Behaviour cloning. A model trained on these trajectories imitates the behaviour of the source optimizers; it inherits their inductive biases and failure modes rather than surpassing them by construction.
• Coverage. Although broad, the benchmark families skew toward AutoML-style problems (HPO/NAS) plus synthetic functions, and may under-represent other real-world domains.

Citation

If you use BBO-Pile, please cite:

@article{klein2026bbopile,
 title   = {An Open-Source Training Dataset for Foundation Models for Black-box Optimization},
 author  = {Klein, Aaron and Rakotoarison, Herilalaina and Thale-Bombien, Luca and Salinas, David},
 journal = {arXiv preprint arXiv:2605.23417},
 year    = {2026},
 url     = {https://arxiv.org/abs/2605.23417}
 }

Authors

Aaron Klein (ELLIS Institute Tübingen), Herilalaina Rakotoarison (University of Helsinki), Luca Thale-Bombien (Leipzig University, ScaDS.AI), and David Salinas (ELLIS Institute Tübingen, Prior Labs).