Add BAxUS generator for high-dimensional Bayesian optimization

[gian21391]

Implements BAxUS (Papenmeier et al., NeurIPS 2022) for single-objective problems where most input dimensions are irrelevant. Optimization happens inside a sparse random embedding that expands whenever the trust region collapses, so a run starts cheap in a few dimensions and only pays for more as it earns them.

from xopt.generators.bayesian import BAxUSGenerator

generator = BAxUSGenerator(
    vocs=vocs,             # 100 continuous variables, 3 of which matter
    target_dim_init=2,     # start in a 2-D subspace
    seed=0,
    eval_budget=60,        # total planned evaluations — paces the expansion schedule
)

On a 100-D sphere with 3 effective dimensions the embedding grows 2 → 8 → 32 over 25 steps. The generator draws its own Sobol seed points, so no random_evaluate is needed first. Set eval_budget to the number of planned evaluations — without it the reference expansion schedule is replaced by a ceil(target_dim / 2) heuristic that expands far more slowly.

Scope — narrower than the other Bayesian generators

The GP lives in the embedded subspace rather than in VOCS space, so anything keyed to VOCS-space columns can't be honored. Constraints, observables, discrete and contextual variables, fixed_features, max_travel_distances, custom_objective, n_interpolate_points and turbo controllers are all rejected at construction rather than silently ignored. It generates one candidate at a time, and visualize_model raises.

Deviations from the reference

target_dim_init is a user knob rather than derived from input dimensionality; the acquisition is the inherited analytic LogEI over the trust-region box rather than Thompson sampling over a masked candidate set; and data not generated through the current embedding is least-squares projected into target space. All three are documented in the module docstring and docs/algorithms.md.

Test

119 tests in xopt/tests/generators/bayesian/test_baxus.py. Beyond ordinary coverage it pins: a _TutorialBaxusState oracle transcribed from the BoTorch tutorial that cross-checks the budget-aware failure-tolerance schedule; checkpoint integrity across dump/restore cycles; trust-region box geometry and that candidates come from the acquisition rather than a constant; lengthscale-weight normalization at target_dim up to 1200, where the naive geometric-mean form underflows; NaN and failed-evaluation ingestion; and every rejected-option path.

Docs: docs/algorithms.md entry, API reference page, README/index entries, and a runnable notebook covering the 100-D example plus checkpoint/resume.

[nikitakuklev]

Hi Gianluca,

Without reviewing the PR, I will say this quite plainly: we are not going to accept code that is direct Claude slop.

Obviously everyone is using agentic harnesses. I myself go through a disturbing amount of tokens every month. But to avoid sloppification, you have to fight against the absurd 'gazillion tests + defensive check everything' style of default Claude.

[gian21391]

Hi Nikita, fair enough. I have pushed a commit to simplify the code. I think it is pretty readable now but I would like to do one more pass to check whether the design can be improved. The tests are extensive but not absurd anymore. I have tried to keep the coverage to 99%.

[codecov]

Codecov Report

❌ Patch coverage is 98.97040% with 8 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
xopt/tests/generators/bayesian/test_baxus.py	99.00%	2 Missing and 3 partials ⚠️
xopt/generators/bayesian/baxus.py	98.89%	1 Missing and 2 partials ⚠️

📢 Thoughts on this report? Let us know!

[nikitakuklev]

Thanks, and no worries getting internals too polished - my biggest concern was/is docs text, because that is user-facing maybe-a-bit-verbose-opus-smell part. I'll run it through my opinionated fable/sol review loop before merge as well.