optuna.samplers

The samplers module defines a base class for parameter sampling as described extensively in BaseSampler. The remaining classes in this module represent child classes, deriving from BaseSampler, which implement different sampling strategies.

See also

If you are unsure about which sampler to use, please consider using AutoSampler, which automatically selects a sampler during optimization. For more detail, see the article on AutoSampler.

	`AutoSampler`	`RandomSampler`	`TPESampler`	`GPSampler`	`CmaEsSampler`	`NSGAIISampler`	`NSGAIIISampler`	`GridSampler`	`QMCSampler`	`BoTorchSampler`	`BruteForceSampler`
Float parameters	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\) (\(\color{red}\times\) for infinite domain)
Integer parameters	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\color{green}\checkmark\)
Categorical parameters	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\color{green}\checkmark\)
Pruning	\(\blacktriangle\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\color{red}\times\) (\(\blacktriangle\) for single-objective)	\(\color{red}\times\) (\(\blacktriangle\) for single-objective)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\color{green}\checkmark\)
Multivariate optimization	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\color{green}\checkmark\)	\(\blacktriangle\)
Conditional search space	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\blacktriangle\)	\(\color{green}\checkmark\)
Multi-objective optimization	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{red}\times\)	\(\color{green}\checkmark\) (\(\blacktriangle\) for single-objective)	\(\color{green}\checkmark\) (\(\blacktriangle\) for single-objective)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)
Batch optimization	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)
Distributed optimization	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\blacktriangle\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)
Constrained optimization	\(\color{green}\checkmark\)	\(\color{red}\times\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{red}\times\)	\(\color{green}\checkmark\)	\(\color{green}\checkmark\)	\(\color{red}\times\)	\(\color{red}\times\)	\(\color{green}\checkmark\)	\(\color{red}\times\)
Time complexity (per trial) (*)	N/A	\(O(d)\)	\(O(dn \log n)\)	\(O(n^3)\)	\(O(d^3)\)	\(O(mp^2)\) (***)	\(O(mp^2)\) (***)	\(O(dn)\)	\(O(dn)\)	\(O(n^3)\)	\(O(d)\)
Recommended budgets (#trials) (**)	as many as one likes	as many as one likes	100–1000	–500	1000–10000	100–10000	100–10000	number of combinations	as many as one likes	10–100	number of combinations

Note

\(\color{green}\checkmark\): Supports this feature. \(\blacktriangle\): Works, but inefficiently. \(\color{red}\times\): Causes an error, or has no interface.

(*): We assumes that \(d\) is the dimension of the search space, \(n\) is the number of finished trials, \(m\) is the number of objectives, and \(p\) is the population size (algorithm specific parameter). This table shows the time complexity of the sampling algorithms. We may omit other terms that depend on the implementation in Optuna, including \(O(d)\) to call the sampling methods and \(O(n)\) to collect the completed trials. This means that, for example, the actual time complexity of RandomSampler is \(O(d+n+d) = O(d+n)\). From another perspective, with the exception of NSGAIISampler and NSGAIIISampler, all time complexity is written for single-objective optimization.

(**): (1) The budget depends on the number of parameters and the number of objectives. (2) This budget includes n_startup_trials if a sampler has n_startup_trials as one of its arguments.

(***): This time complexity assumes that the number of population size \(p\) and the number of parallelization are regular. This means that the number of parallelization should not exceed the number of population size \(p\).

Note

Samplers initialize their random number generators by specifying seed argument at initialization. However, samplers reseed them when n_jobs!=1 of optuna.study.Study.optimize() to avoid sampling duplicated parameters by using the same generator. Thus we can hardly reproduce the optimization results with n_jobs!=1. For the same reason, make sure that use either seed=None or different seed values among processes with distributed optimization explained in Easy Parallelization tutorial.

Note

For float, integer, or categorical parameters, see Pythonic Search Space tutorial.

For pruning, see Efficient Optimization Algorithms tutorial.

For multivariate optimization, see BaseSampler. The multivariate optimization is implemented as sample_relative() in Optuna. Please check the concrete documents of samplers for more details.

For conditional search space, see Pythonic Search Space tutorial and TPESampler. The group option of TPESampler allows TPESampler to handle the conditional search space.

For multi-objective optimization, see Multi-objective Optimization with Optuna tutorial.

For batch optimization, see Batch Optimization tutorial. Note that the constant_liar option of TPESampler allows TPESampler to handle the batch optimization.

For distributed optimization, see Easy Parallelization tutorial. Note that the constant_liar option of TPESampler allows TPESampler to handle the distributed optimization.

For constrained optimization, see an example.

`BaseSampler`	Base class for samplers.
`RandomSampler`	Sampler using random sampling.
`TPESampler`	Sampler using TPE (Tree-structured Parzen Estimator) algorithm.
`GPSampler`	Sampler using Gaussian process-based Bayesian optimization.
`CmaEsSampler`	A sampler using cmaes as the backend.
`NSGAIISampler`	Multi-objective sampler using the NSGA-II algorithm.
`NSGAIIISampler`	Multi-objective sampler using the NSGA-III algorithm.
`GridSampler`	Sampler using grid search.
`QMCSampler`	A Quasi Monte Carlo Sampler that generates low-discrepancy sequences.
`BruteForceSampler`	Sampler using brute force.
`PartialFixedSampler`	Sampler with partially fixed parameters.

Note

The following optuna.samplers.nsgaii module defines crossover operations used by NSGAIISampler.

optuna.samplers.nsgaii