RandomSearchOptimizer

class RandomSearchOptimizer(search_space: dict[str, list], initialize: dict[Literal['grid', 'vertices', 'random', 'warm_start'], int | list[dict]] = None, constraints: list[callable] = None, random_state: int = None, nth_process: int = None)[source]

Simple optimizer that samples random positions from the search space.

Random Search is the simplest optimization strategy that samples positions uniformly at random from the search space. Despite its simplicity, random search is surprisingly effective for many problems, especially in high dimensions where it can outperform grid search due to better coverage of important dimensions.

The algorithm has no memory of previous evaluations and makes no assumptions about the objective function. Each iteration independently samples a random point, making it trivially parallelizable and resistant to getting stuck in local optima.

The algorithm is well-suited for:

High-dimensional search spaces (avoids curse of dimensionality)
Baseline comparison for other optimization methods
Initial exploration before applying more sophisticated methods
Problems with many irrelevant dimensions
Embarrassingly parallel optimization scenarios

Random search is often recommended as a first approach for hyperparameter optimization due to its simplicity and effectiveness. It provides uniform coverage of the search space without requiring any tuning parameters.

Parameters:

search_spacedict[str, list]

The search space to explore, defined as a dictionary mapping parameter names to arrays of possible values.

Each key is a parameter name (string), and each value is a numpy array or list of discrete values that the parameter can take. The optimizer will only evaluate positions that are on this discrete grid.

Example: A 2D search space with 100 points per dimension:

search_space = {
    "x": np.linspace(-10, 10, 100),
    "y": np.linspace(-10, 10, 100),
}

The resolution of each dimension (number of points in the array) directly affects optimization quality and speed. More points give finer resolution but increase the search space size exponentially.

initializedict[str, int], default={“vertices”: 4, “random”: 2}

Strategy for generating initial positions before the main optimization loop begins. Initialization samples are evaluated first, and the best one becomes the starting point for the optimizer.

Supported keys:

"grid": int – Number of positions on a regular grid.
"vertices": int – Number of corner/edge positions of the search space.
"random": int – Number of uniformly random positions.
"warm_start": list[dict] – Specific positions to evaluate, each as a dict mapping parameter names to values.

Multiple strategies can be combined:

initialize = {"vertices": 4, "random": 10}
initialize = {"warm_start": [{"x": 0.5, "y": 1.0}], "random": 5}

More initialization samples improve the starting point but consume iterations from n_iter. For expensive objectives, a few targeted warm-start points are often more efficient than many random samples.

constraintslist[callable], default=[]

A list of constraint functions that restrict the search space. Each constraint is a callable that receives a parameter dictionary and returns True if the position is valid, False if it should be rejected.

Rejected positions are discarded and regenerated: the optimizer resamples a new candidate position (up to 100 retries per step). During initialization, positions that violate constraints are filtered out entirely.

Example: Constrain the search to a circular region:

def circular_constraint(para):
    return para["x"]**2 + para["y"]**2 <= 25

constraints = [circular_constraint]

Multiple constraints are combined with AND logic (all must return True).

random_stateint or None, default=None

Seed for the random number generator to ensure reproducible results.

None: Use a new random state each run (non-deterministic).
int: Seed the random number generator for reproducibility.

Setting a fixed seed is recommended for debugging and benchmarking. Different seeds may lead to different optimization trajectories, especially for stochastic optimizers.

Attributes:

best_para: Return the best parameters found as a dictionary.
best_value: Return the best values found (raw parameter values).
search_data: Lazily construct and return the search results DataFrame.

Methods

search(objective_function, n_iter[, ...])

Run the optimization loop.

eval_time
init_stats
iter_time

See also

GridSearchOptimizer: Systematic exhaustive search on a regular grid.
RandomAnnealingOptimizer: Starts with large random steps and narrows over time.
BayesianOptimizer: Sample-efficient alternative that builds a surrogate model.

Notes

At each iteration, the algorithm independently samples a uniformly random position from the search space:

\[\begin{split}x_t \\sim \\text{Uniform}(\\text{search\\_space})\end{split}\]

Random search has no memory of previous evaluations. Each sample is independent, making it trivially parallelizable and immune to local optima traps. Research has shown that random search is more efficient than grid search in high dimensions because it provides better coverage of each individual dimension.

Time complexity per iteration is O(d), where d is the number of dimensions.

For visual explanations and comparisons, see the Random Search user guide.

Examples

>>> import numpy as np
>>> from gradient_free_optimizers import RandomSearchOptimizer

>>> def objective(para):
...     return -(para["x"] ** 2 + para["y"] ** 2)

>>> search_space = {
...     "x": np.linspace(-10, 10, 100),
...     "y": np.linspace(-10, 10, 100),
... }

>>> opt = RandomSearchOptimizer(search_space)
>>> opt.search(objective, n_iter=1000)

search(objective_function: Callable[[dict[str, Any]], float], n_iter: int, max_time: float | None = None, max_score: float | None = None, early_stopping: dict[str, Any] | None = None, memory: bool = True, memory_warm_start: pd.DataFrame | None = None, verbosity: list[str] | Literal[False] = ['progress_bar', 'print_results', 'print_times'], optimum: Literal['maximum', 'minimum'] = 'maximum', callbacks: list[Callable[[CallbackInfo], bool | None]] | None = None, catch: dict[type[Exception], int | float] | None = None) → None[source]

Run the optimization loop.

Evaluates objective_function up to n_iter times, searching for the parameters that maximize (or minimize) the returned score. The search proceeds in two phases: an initialization phase that evaluates starting positions (controlled by the initialize constructor parameter), followed by an iteration phase where the optimizer’s strategy generates new candidate positions.

After the search finishes, results are available via best_para, best_score, and search_data.

Parameters:

objective_functioncallable

The function to optimize. Must accept a single dictionary mapping parameter names to values and return either:

A float score, or
A tuple (float, dict) where the second element contains custom metrics (accessible via callbacks and search_data).

Example:

def objective(params):
    return -(params["x"] ** 2 + params["y"] ** 2)

def objective_with_metrics(params):
    loss = params["x"] ** 2
    return -loss, {"loss": loss}

n_iterint

Total number of iterations (including initialization). Each iteration evaluates the objective function once (unless a cached result is found when memory=True).

max_timefloat or None, default=None

Maximum wall-clock time in seconds. The search stops after the current iteration if the elapsed time exceeds this limit. None means no time limit.

max_scorefloat or None, default=None

Target score threshold. The search stops when the best score found so far reaches or exceeds this value. When optimum="minimum", this refers to the original (non-negated) score. None means no score limit.

early_stoppingdict or None, default=None

Configuration for stopping the search when progress stalls. None disables early stopping. When provided, the dictionary supports the following keys:

"n_iter_no_change" (int, required): Stop if no improvement is observed for this many consecutive iterations.
"tol_abs" (float, optional): Minimum absolute improvement required over the window to count as progress.
"tol_rel" (float, optional): Minimum relative improvement (in percent) required over the window to count as progress.

Example:

early_stopping = {"n_iter_no_change": 50}
early_stopping = {"n_iter_no_change": 30, "tol_abs": 0.001}

memorybool, default=True

If True, cache objective function evaluations in an in-memory dictionary keyed by position. When the optimizer revisits a previously evaluated position, the cached score is returned without calling the objective function again. This is especially useful for discrete search spaces where revisits are common.

memory_warm_startpd.DataFrame or None, default=None

A DataFrame from a previous search (typically obtained via search_data) to pre-populate the evaluation cache. The DataFrame must contain columns matching the search space parameter names plus a "score" column. Requires memory=True.

Example:

opt1 = HillClimbingOptimizer(search_space)
opt1.search(objective, n_iter=50)

opt2 = HillClimbingOptimizer(search_space)
opt2.search(objective, n_iter=50,
            memory_warm_start=opt1.search_data)

verbositylist[str] or False, default=[“progress_bar”, “print_results”, “print_times”]

Controls console output during and after the search. Pass False or an empty list for silent operation.

Supported values:

"progress_bar": Show a live tqdm progress bar during the search.
"print_results": Print best score and best parameters after the search completes.
"print_times": Print timing breakdown (evaluation time, optimization overhead, throughput) after the search completes.
"print_search_stats": Print search statistics including iteration counts, acceptance rate, number of improvements, and longest plateau.
"print_statistics": Print score statistics (min, max, mean, std) after the search completes.
"debug_stop": Print detailed stopping condition debug info when the search terminates early.

optimum{“maximum”, “minimum”}, default=”maximum”

Whether to maximize or minimize the objective function. When set to "minimum", the objective function’s return value is negated internally so that the optimizer always maximizes. The reported best_score is in original (non-negated) units.

callbackslist[callable] or None, default=None

A list of callback functions invoked after each iteration. Each callback receives a single argument info with the following attributes:

info.iteration (int): Current iteration index (0-based).
info.score (float): Score from the current evaluation.
info.params (dict): Parameters evaluated in this iteration.
info.best_score (float): Best score found so far.
info.best_para (dict): Parameters of the best score.
info.n_iter (int): Total iterations planned.
info.phase (str): "init" or "iter".
info.elapsed_time (float): Seconds since search started.
info.metrics (dict): Custom metrics from the objective function (empty if the objective returns only a score).
info.convergence (list[float]): Best score at each iteration so far.

If any callback returns False, the search stops immediately. Any other return value (including None) is ignored and the search continues.

Example:

def log_progress(info):
    if info.iteration % 10 == 0:
        print(f"Iter {info.iteration}: best={info.best_score:.4f}")

def stop_early(info):
    if info.best_score > 0.99:
        return False  # stops the search

opt.search(objective, n_iter=100,
           callbacks=[log_progress, stop_early])

catchdict[type, float] or None, default=None

Error handling for the objective function. Maps exception types to fallback scores. When the objective function raises a caught exception, the optimizer records the fallback score instead of crashing. Exception subclasses are matched via isinstance, so {Exception: ...} catches all.

The fallback score is in the user’s original units (before any negation from optimum="minimum"). Use float('nan') or float('inf') to mark positions as invalid without inventing an artificial score.

Example:

catch = {ValueError: -1000, RuntimeError: float('nan')}

opt.search(objective, n_iter=100, catch=catch)

Examples

Basic usage with default settings:

>>> import numpy as np
>>> from gradient_free_optimizers import HillClimbingOptimizer
>>> def objective(para):
...     return -(para["x"] ** 2)
>>> search_space = {"x": np.linspace(-10, 10, 100)}
>>> opt = HillClimbingOptimizer(search_space)
>>> opt.search(objective, n_iter=30)

Using multiple stopping conditions:

>>> opt.search(
...     objective,
...     n_iter=1000,
...     max_time=60,
...     max_score=-0.01,
...     early_stopping={"n_iter_no_change": 50},
... )

property best_para[source]

Return the best parameters found as a dictionary.

Uses the Converter to transform the best position into user-friendly parameter names and values.

Returns:

dict or None: Dictionary mapping parameter names to their best values, or None if no evaluation has been performed yet.

property best_value[source]

Return the best values found (raw parameter values).

Returns:

list or None: List of best values in parameter order, or None if no evaluation has been performed yet.

property search_data: pd.DataFrame[source]

Lazily construct and return the search results DataFrame.

The DataFrame is only built when this property is accessed, avoiding a large memory spike at the end of high-dimensional optimizations. The result is cached so subsequent accesses don’t rebuild it.