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From Sequential to Massively-Parallel Bayesian Optimization#
Author(s): Romain Egele.
This example demonstrates the advantages of parallel evaluations over sequential
evaluations with Bayesian optimization. We start by defining a black-box run-function that
implements the Ackley function:
To help illustrate the parallelization gain, we will simulate a computational cost
by using time.sleep. We also use the @profile decorator to collect starting/ending
times of each call to the run-function. When using this decorator, the run-function will
return a dictionnary including "metadata" with 2 new keys "timestamp_start" and
"timestamp_end". The run-function is defined in a separate Python module
for better serialization (through pickle) in case other parallel backends such as "process" would be used
"""Set of Black-Box functions useful to build examples."""
import time
import numpy as np
from deephyper.evaluator import profile
def ackley(x, a=20, b=0.2, c=2 * np.pi):
d = len(x)
s1 = np.sum(x**2)
s2 = np.sum(np.cos(c * x))
term1 = -a * np.exp(-b * np.sqrt(s1 / d))
term2 = -np.exp(s2 / d)
y = term1 + term2 + a + np.exp(1)
return y
@profile
def run_ackley(config, sleep_loc=2, sleep_scale=0.5):
# to simulate the computation of an expensive black-box
if sleep_loc > 0:
t_sleep = np.random.normal(loc=sleep_loc, scale=sleep_scale)
t_sleep = max(t_sleep, 0)
time.sleep(t_sleep)
x = np.array([config[k] for k in config if "x" in k])
x = np.asarray_chkfinite(x) # ValueError if any NaN or Inf
return -ackley(x) # maximisation is performed
After defining the run-function we can continue with the definition of our optimization script:
import black_box_util as black_box
import matplotlib.pyplot as plt
from deephyper.analysis import figure_size
from deephyper.analysis.hpo import plot_search_trajectory_single_objective_hpo
from deephyper.analysis.hpo import plot_worker_utilization
from deephyper.evaluator import Evaluator
from deephyper.evaluator.callback import TqdmCallback
from deephyper.hpo import HpProblem, CBO, RandomSearch
Then, we define the variable(s) we want to optimize. For this problem we
optimize Ackley in a N-dimensional search space. Each dimension in the continuous range
[-32.768, 32.768]. The true minimum is located at (0, ..., 0).
nb_dim = 5
problem = HpProblem()
for i in range(nb_dim):
problem.add_hyperparameter((-32.768, 32.768), f"x{i}")
problem
Configuration space object:
Hyperparameters:
x0, Type: UniformFloat, Range: [-32.768, 32.768], Default: 0.0
x1, Type: UniformFloat, Range: [-32.768, 32.768], Default: 0.0
x2, Type: UniformFloat, Range: [-32.768, 32.768], Default: 0.0
x3, Type: UniformFloat, Range: [-32.768, 32.768], Default: 0.0
x4, Type: UniformFloat, Range: [-32.768, 32.768], Default: 0.0
Then, we define some default search parameters for the Centralized Bayesian Optimization (CBO) algorithm.
search_kwargs = {
"n_initial_points": 2 * nb_dim + 1, # Number of initial random points
"surrogate_model": "ET", # Use Extra Trees as surrogate model
"surrogate_model_kwargs": {
"n_estimators": 25, # Relatively small number of trees in the surrogate to make it "fast"
"min_samples_split": 8, # Larger number to avoid small leaf nodes (smoothing the response)
},
"multi_point_strategy": "qUCBd", # Multi-point strategy for asynchronous batch generations (explained later)
"acq_optimizer": "ga", # Use continuous Genetic Algorithm for the acquisition function optimizer
"acq_optimizer_freq": 1, # Frequency of the acquisition function optimizer (1 = each new batch generation) increasing this value can help amortize the computational cost of acquisition function optimization
"filter_duplicated": False, # Deactivate filtration of duplicated new points
"kappa": 10.0, # Initial value of exploration-exploitation parameter for the acquisition function
"scheduler": { # Scheduler for the exploration-exploitation parameter "kappa"
"type": "periodic-exp-decay", # Periodic exponential decay
"period": 50, # Period over which the decay is applied. It is useful to escape local solutions.
"kappa_final": 0.001 # Value of kappa at the end of each "period"
},
"random_state": 42, # Random seed
}
Then, we define the time budget for the optimization. We will compare the performance of a sequential search with a parallel search for the same time budget. The time budget is defined in seconds.
timeout = 60 # 1 minute
Then, we define the sequential Bayesian optimization search.
sequential_search = CBO(problem, black_box.run_ackley, **search_kwargs)
WARNING:root:Results file already exists, it will be renamed to /Users/romainegele/Documents/Argonne/deephyper/examples/results_20250103-120409.csv
The previously simplified definition of the search is equivalent to the following:
sequential_evaluator = Evaluator.create(
black_box.run_ackley,
method="thread", # For synchronous function defintion relying on the GIL or I/O bound tasks
method_kwargs={
"num_workers": 1,
"callbacks": [TqdmCallback()]
},
)
sequential_search = CBO(problem, sequential_evaluator, **search_kwargs)
Where we use the "thread"-evaluator with a single worker and use the TqdmCallback to display
a progress bar during the search.
We can now run the sequential search for 2 minutes. The call to the search-method will return a
DataFrame with the results of the search.
If this step is executed multiple times without creating a new search the results will be accumulated in the same DataFrame.
results = {}
results["sequential"] = sequential_search.search(timeout=timeout)
offset = results["sequential"]["m:timestamp_start"].min()
results["sequential"]["m:timestamp_end"] -= offset
results["sequential"]["m:timestamp_start"] -= offset
results["sequential"]
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Each row of the DataFrame corresponds to an evaluation of the run-function. The DataFrame contains the following columns:
- "p:*": The parameters of the search space.
- "objective": The objective value returned by the evaluation.
- "job_id": The id of the evaluation in increasing order of job creation.
- "job_status": The status of the evaluation (e.g., “DONE”, “CANCELLED”).
- "m:timestamp_submit/gather": The submition and gathering times of the evaluation by the Evaluator (includes overheads).
- "m:timestamp_start/end": The starting and ending time of the evaluation.
We can now plot the results of the sequential search. The first plot shows the evolution of the objective. The second plot shows the utilization of the worker over time.
fig, axes = plt.subplots(
nrows=2,
ncols=1,
sharex=True,
figsize=figure_size(width=600),
)
plot_search_trajectory_single_objective_hpo(
results["sequential"], mode="min", x_units="seconds", ax=axes[0]
)
plot_worker_utilization(
results["sequential"], num_workers=1, profile_type="start/end", ax=axes[1]
)
plt.tight_layout()
plt.show()
/Users/romainegele/Documents/Argonne/deephyper/examples/plot_from_serial_to_parallel_hpo.py:134: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
plt.show()
Then, we can create a parallel evaluator with 100 workers.
parallel_evaluator = Evaluator.create(
black_box.run_ackley,
method="thread",
method_kwargs={
"num_workers": 100, # For the parallel evaluations
"callbacks": [TqdmCallback()]
},
)
parallel_search = CBO(problem, parallel_evaluator, **search_kwargs)
WARNING:root:Results file already exists, it will be renamed to /Users/romainegele/Documents/Argonne/deephyper/examples/results_20250103-120512.csv
The parallel search is executed for 1 minute.
results["parallel"] = parallel_search.search(timeout=timeout)
offset = results["parallel"]["m:timestamp_start"].min()
results["parallel"]["m:timestamp_start"] -= offset
results["parallel"]["m:timestamp_end"] -= offset
results["parallel"]
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It can be surprising to see in the results that the last lines have "job_status" set to “CANCELLED” but
still have an objective value. This is due to the fact that the cancellation of a job is asynchronous and already scheduled Asyncio tasks are therefore executed. When the timeout is reached the jobs created by the “thread” method jobs cannot be directly killed but rather their job.status is updated to "CANCELLING" and the user-code is responsible for checking the status of the job and interrupting the execution. This is why the objective value is still present in the results. This behavior is different from the “process” method where the jobs are killed directly.
We can now plot the results of the parallel search. The first plot shows the evolution of the objective. The second plot shows the utilization of the worker over time.
We can see that the parallel search is able to evaluate a lot more points in the same time budget. This also allows the algorithm to explore more of the search space and potentially find better solutions. The utilization plot shows that the workers are used efficiently in the parallel search (above 80%).
fig, axes = plt.subplots(
nrows=2,
ncols=1,
sharex=True,
figsize=figure_size(width=600),
)
plot_search_trajectory_single_objective_hpo(
results["parallel"], mode="min", x_units="seconds", ax=axes[0]
)
plot_worker_utilization(
results["parallel"], num_workers=1, profile_type="start/end", ax=axes[1]
)
plt.tight_layout()
plt.show()
/Users/romainegele/Documents/Argonne/deephyper/examples/plot_from_serial_to_parallel_hpo.py:182: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
plt.show()
Finally, we compare both search with the execution time is used as the x-axis. The advantage of parallelism is clearly visible by the difference in the number of evaluations and in objective.
fig, ax = plt.subplots(figsize=figure_size(width=600))
for i, (strategy, df) in enumerate(results.items()):
plot_search_trajectory_single_objective_hpo(
df,
show_failures=False,
mode="min",
x_units="seconds",
ax=ax,
label=strategy,
plot_kwargs={"color": f"C{i}"},
scatter_success_kwargs={"color": f"C{i}"},
)
plt.xlabel("Time (sec.)")
plt.ylabel("Objective")
plt.yscale("log")
plt.grid(visible=True, which="minor", linestyle=":")
plt.grid(visible=True, which="major", linestyle="-")
plt.legend()
plt.show()
/Users/romainegele/Documents/Argonne/deephyper/examples/plot_from_serial_to_parallel_hpo.py:208: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
plt.show()
Finally, one could compare to a random search to see if the overheads of the parallel Bayesian optimization are worth it (i.e., the cost of fitting and optimizing the surrogate model). The evaluator is defined similarly to the one used for the parallel Bayesian optimization search:
parallel_evaluator = Evaluator.create(
black_box.run_ackley,
method="thread",
method_kwargs={
"num_workers": 100, # For the parallel evaluations
"callbacks": [TqdmCallback()]
},
)
random_search = RandomSearch(problem, parallel_evaluator, random_state=search_kwargs["random_state"])
results["random"] = random_search.search(timeout=timeout)
offset = results["random"]["m:timestamp_start"].min()
results["random"]["m:timestamp_start"] -= offset
results["random"]["m:timestamp_end"] -= offset
results["random"]
WARNING:root:Results file already exists, it will be renamed to /Users/romainegele/Documents/Argonne/deephyper/examples/results_20250103-120616.csv
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The number of evaluations of the random search is higher than the parallel Bayesian optimization search.
print(f"Number of evaluations for the parallel Bayesian optimization: {len(results['parallel'])}")
print(f"Number of evaluations for the random search: {len(results['random'])}")
Number of evaluations for the parallel Bayesian optimization: 2477
Number of evaluations for the random search: 3012
The utilization of the worker is confirmed to be near 100% for the random search.
fig, axes = plt.subplots(
nrows=2,
ncols=1,
sharex=True,
figsize=figure_size(width=600),
)
plot_search_trajectory_single_objective_hpo(
results["random"], mode="min", x_units="seconds", ax=axes[0]
)
plot_worker_utilization(
results["random"], num_workers=1, profile_type="start/end", ax=axes[1]
)
plt.tight_layout()
plt.show()
/Users/romainegele/Documents/Argonne/deephyper/examples/plot_from_serial_to_parallel_hpo.py:254: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
plt.show()
However, the objective value of the parallel Bayesian optimization search is significantly better than the random search.
# sphinx_gallery_thumbnail_number = 5
fig, ax = plt.subplots(figsize=figure_size(width=600))
labels = {
"random": "Parallel Random Search",
"sequential": "Sequential Bayesian Optimization",
"parallel": "Parallel Bayesian Optimization",
}
for i, (key, label) in enumerate(labels.items()):
df = results[key]
plot_search_trajectory_single_objective_hpo(
df,
show_failures=False,
mode="min",
x_units="seconds",
ax=ax,
label=label,
plot_kwargs={"color": f"C{i}"},
scatter_success_kwargs={"color": f"C{i}", "alpha": 0.5},
)
plt.xlabel("Time (sec.)")
plt.ylabel("Objective")
plt.yscale("log")
plt.grid(visible=True, which="minor", linestyle=":")
plt.grid(visible=True, which="major", linestyle="-")
plt.legend()
plt.show()
/Users/romainegele/Documents/Argonne/deephyper/examples/plot_from_serial_to_parallel_hpo.py:285: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
plt.show()
Total running time of the script: (3 minutes 10.287 seconds)