quantecarlo 0.1.1

Batch Bayesian optimization sampler (q-EI) for Optuna, backed by a remote GP service

quantecarlo

Batch Bayesian optimization for Optuna using q-Expected Improvement (q-EI). Drop in one sampler, point it at a hosted GP endpoint, and get a batch of q well-chosen candidates back per iteration instead of one at a time.

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Quickstart

pip install quantecarlo

import warnings
from concurrent.futures import ThreadPoolExecutor

import optuna
from optuna.trial import TrialState

from quantecarlo import DimSpec, qEISampler

# The DimSpec names and bounds must match the suggest_* calls in the objective.
search_space = [
    DimSpec(name="x", type="float", low=-5.0, high=5.0),
    DimSpec(name="y", type="float", low=-5.0, high=5.0),
]

Q = 4               # batch size; also the number of parallel workers
N_STARTUP = 8       # random warm-up trials before the GP kicks in
N_ITERATIONS = 10   # total trials = N_ITERATIONS × Q

def objective(trial: optuna.Trial) -> float:
    x = trial.suggest_float("x", -5.0, 5.0)
    y = trial.suggest_float("y", -5.0, 5.0)
    return (x - 1.3) ** 2 + (y + 0.7) ** 2   # minimum at (1.3, -0.7)

sampler = qEISampler(search_space=search_space, q=Q, n_startup_trials=N_STARTUP)
study = optuna.create_study(direction="minimize", sampler=sampler)
optuna.logging.set_verbosity(optuna.logging.WARNING)

with ThreadPoolExecutor(max_workers=Q) as executor:
    for _ in range(N_ITERATIONS):
        # Ask Q times first — the first ask fires the API and fills the cache,
        # the remaining Q-1 asks pop from the cache without a second API call.
        trials = [study.ask() for _ in range(Q)]

        # Evaluate the batch in parallel, then tell results back.
        futures = {executor.submit(objective, t): t for t in trials}
        for future, trial in futures.items():
            try:
                study.tell(trial, future.result())
            except Exception as exc:
                warnings.warn(str(exc))
                study.tell(trial, state=TrialState.FAIL)

print(study.best_params)

Why ask-tell instead of study.optimize?

The ask-tell loop is the pattern Optuna uses internally, exposed here explicitly so the sampler can coordinate across parallel workers. With study.optimize(n_jobs=q), each worker thread calls sample_relative independently — the sampler has no visibility into what the other q-1 workers are about to evaluate. The result is that all q suggestions are drawn from the same posterior snapshot, and candidates often cluster.

The ask-tell pattern fixes this: all q asks happen before any evaluation begins. The first ask triggers one API call that selects q jointly diverse candidates; asks 2 through q pop from the local cache. When the evaluations finish and tell reports the results, the next round starts with a fully updated posterior. This is what makes the joint q-EI criterion meaningful in practice.

Additional examples are in the demos/ directory:

• demos/demo.py — NAS on the breast-cancer dataset using an MLP, with explicit batching and a per-iteration progress table.
• demos/demo7.py — comparison of qEISampler (ask-tell) against Optuna's default TPE on a pool-based image ad search task. Requires external data files (not included).

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What's happening under the hood (you don't need to touch any of this)

Each time the local suggestion cache runs dry, qEISampler POSTs your observed (X, y) pairs to a remote GP service. That service:

1. Normalises each parameter to [0, 1] (log-scale for log=True dims).
2. Rank-transforms y to standard-normal via the Probability Integral Transform — so the GP always sees well-behaved Gaussian targets regardless of the shape of your objective's distribution.
3. Fits an ExactGP (Matérn-5/2 ARD kernel) on a GPU via Adam on the marginal log-likelihood.
4. Draws n_candidates random candidate batches of size q and scores each batch jointly with q-EI.
5. Returns the highest-scoring batch decoded back to your original parameter scale. Int dims are snapped to the nearest integer.

The sampler then hands out one candidate per study.ask() call from the local cache. The next API call doesn't fire until the cache is exhausted — so q threads share a single round-trip.

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Parameters

DimSpec

Describes one dimension of your search space.

Field	Type	Description
name	str	Must match the corresponding suggest_* call in your objective.
type	"float" | "int"	Continuous float or integer. Int dims are snapped on decode.
low	float	Lower bound (inclusive).
high	float	Upper bound (inclusive).
log	bool	Log-uniform sampling. Use for parameters that span orders of magnitude (learning rates, weight decay). Default False.
step	float | None	Grid step for int dims. Default 1.

Categorical dimensions are not yet supported.

qEISampler

Parameter	Default	Description
search_space	—	List of DimSpec, one per hyperparameter.
api_url	(hosted)	GP endpoint URL. Override only if self-hosting.
n_startup_trials	8	Number of random trials before the GP is used. Too few observations make GP fitting unreliable.
q	4	Batch size. Set n_jobs=q in study.optimize to evaluate the batch in parallel.
n_candidates	512	Random candidate batches scored per API call. Larger = better coverage; diminishing returns above ~1024 for most spaces.
train_steps	60	Adam steps for GP kernel hyperparameter optimisation. Increase for tighter fits on noisy objectives.
lr	0.1	Adam learning rate for GP training.
xi	0.01	EI exploration bonus. Larger values bias toward uncertain regions; smaller values exploit the current best.
mode	"production"	"debug" returns the full GP posterior surface in the API response — useful for diagnostics.
seed	None	Random seed for the fallback random sampler.
timeout	120.0	HTTP timeout in seconds for the API call.

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Why q-EI instead of just adding more threads?

Running study.optimize(n_jobs=q) with a standard sampler (TPE, random) does parallelize objective evaluation, but each worker samples independently — it has no idea what the other q-1 workers are about to try. You often end up with a batch where several candidates cluster near the same local optimum.

q-EI scores the whole batch jointly. It computes the expected improvement of the best point in the batch over the current best, taking into account the full joint posterior covariance across the q candidates. The optimizer naturally diversifies: a second candidate near an already-selected point contributes little to the joint maximum, so the algorithm spreads the batch across promising but distinct regions.

In practice this means each batch of q trials carries more information than q independently-drawn trials. You cover the space more efficiently and tend to reach good solutions in fewer total function evaluations — which matters when each evaluation is expensive (a training run, an experiment, a simulation).

The cost is one API call per batch (a few seconds for a warm GP endpoint) in exchange for a smarter set of q candidates. That tradeoff is almost always worth it when objective evaluations take more than a minute.