benderopt
benderopt is a black box optimization library.
For asynchronous use, a web client using this library is available in open access at bender.dreem.com
The algorithm implemented "parzen_estimator" is similar to TPE described in: Bergstra, James S., et al. “Algorithms for hyper-parameter optimization.” Advances in Neural Information Processing Systems.
Installation
pip install benderopt
or from the sources
Demo
Here is a comparison on 200 evaluations of a function we want to minimize. First a random estimator is used to select random evaluation point. Then the parzen_estimator implemented in benderopt is used to select evaluation points.
The function to minimize is the following: cos(x) + cos(2 * x + 1) + cos(y).
The red point correspond to the location of the global minima between 0 and 2pi for x and y.
The code to generate the video can be found in benchmark/benchmark_sinus2D
We can observe on this example that the parzen estimator tends to explore more the local minimum than the random approach. This might lead to a better optimization given a fixed number of evaluations.
The goal
In Black box optimization, we have a function to optimize but cannot compute the gradient, and evaluation is expensive in term of time / ressource. So we want to find a good exploration-exploitation trade off to get the best hyperparameters in as few evaluations as possible. Use case are:
- Optimization of a machine learning model (number of layers of a neural network, function of activation, etc.
- Business optimization (marketing campain, a/b testing)
Code Minimal Example
One of the advantage of benderopt is that it uses JSON-like object representation making it easier for a user to define parameters to optimize. This also allows an easy to integratation with an asynchrounous system such as bender.dreem.com.
Here is a minimal example.
from benderopt import minimize
import numpy as np
import logging
logging.basicConfig(level=logging.DEBUG) # logging.INFO will print less information
# We want to minimize the sinus function between 0 and 2pi
def f(x):
return np.sin(x)
# We define the parameters we want to optimize:
optimization_problem_parameters = [
{
"name": "x",
"category": "uniform",
"search_space": {
"low": 0,
"high": 2 * np.pi,
}
}
]
# We launch the optimization
best_sample = minimize(f, optimization_problem_parameters, number_of_evaluation=50)
print(best_sample["x"], 3 * np.pi / 2)
> 4.710390692396651 4.71238898038469
Minimal Documentation:
Optimization Problem
An optimization problem contains:
- A list of parameters (i.e. parameters with their search space)
- A list of observation (i.e. values for each parameter of the list and a corresponding loss)
We use JSON-like representation for each of them e.g.
optimization_problem_data = {
"parameters": [
{
"name": "parameter_1",
"category": "uniform",
"search_space": {"low": 0, "high": 2 * np.pi, "step": 0.1}
},
{
"name": "parameter_2",
"category": "categorical",
"search_space": {"values": ["a", "b", "c"]}
}
],
"observations": [
{
"sample": {"parameter_1": 0.4, "parameter_2": "a"},
"loss": 0.08
},
{
"sample": {"parameter_1": 3.4, "parameter_2": "a"},
"loss": 0.1
},
{
"sample": {"parameter_1": 4.1, "parameter_2": "c"},
"loss": 0.45
},
]
}
Optimizer
An optimizer takes an optimization problem and suggest new_predictions. In other words, an optimizer takes a list of parameters with their search space and a history of past evaluations to suggest a new one.
Using the optimization_problem_data from the previous example:
from benderopt.base import OptimizationProblem, Observation
from benderopt.optimizer import optimizers
optimization_problem = OptimizationProblem.from_json(optimization_problem_data)
optimizer = optimizers["parzen_estimator"](optimization_problem)
sample = optimizer.suggest()
print(sample)
> {"parameter_1": 3.9, "parameter_2": "b"}
Optimizers currently available are random and parzen_estimator.
Benderopt allows to add a new optimizer really easily by inheriting an optimizer from BaseOptimizer class.
You can check benderopt/optimizer/random.py for a minimal example.
Minimize function
Minimize function shown above in the minimal example section implementation is quite strateforward:
optimization_problem = OptimizationProblem.from_list(optimization_problem_parameters)
optimizer = optimizers["parzen_estimator"](optimization_problem)
for _ in range(number_of_evaluation):
sample = optimizer.suggest()
loss = f(**sample)
observation = Observation.from_dict({"loss": loss, "sample": sample})
optimization_problem.add_observation(observation)
The optimization_problem's observation history list is extended with a new observations at each iteration. This allows the optimizer to take them into account for the next suggestion.
Uniform Parameter
| parameter | type | default | comments |
|---|---|---|---|
| low | mandatory | - | lowest possible value: all values will be greater than or equal to low |
| high | mandatory | - | highest value: all values will be stricly less than high |
| step | optionnal | None | discretize the set of possible values: all values will follow 'value = low + k * step with k belonging to [0, K]' |
e.g.
{
"name": "x",
"category": "uniform",
"search_space": {
"low": 0,
"high": 2 * np.pi,
# "step": np.pi / 8
}
}
Log-Uniform Parameter
| parameter | type | default | comments |
|---|---|---|---|
| low | mandatory | - | lowest possible value: all values will be greater than or equal to low |
| high | mandatory | - | highest value: all values will be stricly less than high |
| step | optionnal | None | "discretize the set of possible values: all values will follow 'value = low + k * step with k belonging to [0, K]'" |
| base | optional | 10 | logarithmic base to use |
e.g.
{
"name": "x",
"category": "loguniform",
"search_space": {
"low": 1e-4,
"high": 1e-2,
# "step": 1e-5,
# "base": 10,
}
}
Normal Parameter
| parameter | type | default | comments |
|---|---|---|---|
| low | optionnal | -inf | lowest possible value: all values will be greater than or equal to low |
| high | optionnal | inf | highest value: all values will be stricly less than high |
| mu | mandatory | - | mean value: all values will be initially drawn following a gaussian centered at mu with sigma variance |
| sigma | mandatory | - | sigma value: all values will be initially drawn following a gaussian centered at mu with sigma variance |
| step | optionnal | None | "discretize the set of possible values: all values will follow 'value = low + k * step with k belonging to [0, K]'" |
e.g.
{
"name": "x",
"category": "normal",
"search_space": {
# "low": 0,
# "high": 10,
"mu": 5,
"sigma": 1
# "step": 0.01,
}
}
Log-Normal Parameter
| parameter | type | default | comments |
|---|---|---|---|
| low | optionnal | -inf | lowest possible value: all values will be greater than or equal to low |
| high | optionnal | inf | highest value: all values will be stricly less than high |
| mu | mandatory | - | mean value: all values will be initially drawn following a gaussian centered at mu with sigma variance |
| sigma | mandatory | - | sigma value: all values will be initially drawn following a gaussian centered at mu with sigma variance |
| step | optionnal | None | "discretize the set of possible values: all values will follow 'value = low + k * step with k belonging to [0, K]'" |
| base | optional | 10 | logarithmic base to use |
e.g.
{
"name": "x",
"category": "lognormal",
"search_space": {
# "low": 1e-6,
# "high": 1e0,
"mu": 1e-3,
"sigma": 1e-2
# "step": 1e-7,
# "base": 10,
}
}
Categorical Parameter
| parameter | type | default | comments |
|---|---|---|---|
| values | mandatory | - | list of categories: all values will be sampled from this list |
| probabilities | optionnal | number_of_values * [1 / number_of_values] | list of probabilities: all values will be initially drawn following this probability list |
e.g.
{
"name": "x",
"category": "categorical",
"search_space": {
"values": ["a", "b", "c", "d"],
# "probabilities": [0.1, 0.2, 0.2, 0.2, 0.3]
}
}