Abstract CMA-ES is the gold standard for continuous black-box optimization, but it has diminishing returns: after convergence, additional CMA-ES trials provide little improvement. This sampler addresses that by splitting the trial budget into three phases:
Sobol QMC (8 trials) — quasi-random space-filling initialization CMA-ES (132 trials) — covariance matrix adaptation for main optimization Quasi-random Gaussian refinement (60 trials) — targeted local search around the best point using Sobol-based perturbation vectors with exponentially decaying scale The refinement phase uses quasi-random Sobol sequences transformed via inverse CDF to generate Gaussian-distributed perturbation vectors.
Abstract This package provides an Optuna parallel coordinate plot using Piecewise Cubic Hermite Interpolating Polynomials (Pchip) for smooth, monotonic curves. This reduces visual clutter and makes individual trial trajectories easier to track in high-dimensional spaces compared to standard straight-line plots.
APIs plot_curved_parallel_coordinate(study: optuna.Study, params: list[str] | None = None, points_per_segment: int = 50) -> plotly.graph_objects.Figure study: The optuna.Study object (plots completed trials only). params: List of parameter names to plot. Defaults to all parameters.
Class or Function Names plot_beeswarm(study, *, params=None, target=None, target_name="Objective Value", color_map="RdBu_r", ax=None)
study: An Optuna study with completed trials. params: A list of parameter names to include. If None, all parameters across completed trials are used. target: A callable that extracts a scalar value from a FrozenTrial. Defaults to trial.value. target_name: Label for the x-axis. Defaults to "Objective Value". color_map: Matplotlib colormap name. Defaults to "RdBu_r" (blue for low, red for high).
Abstract This package implements a union search space approach for the multivariate TPE sampler. It enables optimization across conditional or dynamic configurations without forcing independent fallback routines or dropping back to intersection group decompositions. By padding unobserved states with np.nan and dynamically managing categorical distribution dimensions, the sampler successfully estimates a single joint distribution that models correlations between top-level routing choices and nested hyperparameters.
APIs TPEUnionMultivariateSampler(*, n_startup_trials: int = 10, seed: int | None = None) n_startup_trials: The minimum number of completed trials required before the sampler switches from random initialization to Parzen GMM estimation.