# cmaes

This namespace contains the CMAES class, which is a wrapper
for the CMA-ES implementation of the `cma`

package.

##
```
CMAES (SearchAlgorithm, SinglePopulationAlgorithmMixin)
```

¶

This is an interface class between the CMAES implementation
within the `cma`

package developed within the GitHub repository
CMA-ES/pycma.

References:

```
Nikolaus Hansen, Youhei Akimoto, and Petr Baudis.
CMA-ES/pycma on Github. Zenodo, DOI:10.5281/zenodo.2559634,
February 2019.
<https://github.com/CMA-ES/pycma>
Nikolaus Hansen, Andreas Ostermeier (2001).
Completely Derandomized Self-Adaptation in Evolution Strategies.
```

## Source code in `evotorch/algorithms/cmaes.py`

```
class CMAES(SearchAlgorithm, SinglePopulationAlgorithmMixin):
"""
CMAES: Covariance Matrix Adaptation Evolution Strategy.
This is an interface class between the CMAES implementation
within the `cma` package developed within the GitHub repository
CMA-ES/pycma.
References:
Nikolaus Hansen, Youhei Akimoto, and Petr Baudis.
CMA-ES/pycma on Github. Zenodo, DOI:10.5281/zenodo.2559634,
February 2019.
<https://github.com/CMA-ES/pycma>
Nikolaus Hansen, Andreas Ostermeier (2001).
Completely Derandomized Self-Adaptation in Evolution Strategies.
"""
def __init__(
self,
problem: Problem,
*,
stdev_init: RealOrVector, # sigma0
popsize: Optional[int] = None, # popsize
center_init: Optional[Vector] = None, # x0
center_learning_rate: Optional[float] = None, # CMA_cmean
cov_learning_rate: Optional[float] = None, # CMA_on
rankmu_learning_rate: Optional[float] = None, # CMA_rankmu
rankone_learning_rate: Optional[float] = None, # CMA_rankone
stdev_min: Optional[Union[float, np.ndarray]] = None, # minstd
stdev_max: Optional[Union[float, np.ndarray]] = None, # maxstd
separable: bool = False, # CMA_diagonal
obj_index: Optional[int] = None,
cma_options: dict = {},
):
"""
`__init__(...)`: Initialize the CMAES solver.
Args:
problem: The problem object which is being worked on.
stdev_init: Initial standard deviation as a scalar or
as a 1-dimensional array.
popsize: Population size. Can be specified as an int,
or can be left as None to let the CMAES solver
decide the population size according to the length
of a solution.
center_init: Initial center point of the search distribution.
Can be given as a SolutionVector or as a 1-D array.
If left as None, an initial center point is generated
with the help of the problem object's `generate_values(...)`
method.
center_learning_rate: Learning rate for updating the mean
of the search distribution. Leaving this as None
means that the CMAES solver is to use its own default,
which is documented as 1.0.
cov_learning_rate: Learning rate for updating the covariance
matrix of the search distribution. This hyperparameter
acts as a common multiplier for rank_one update and rank_mu
update of the covariance matrix. Leaving this as None
means that the CMAES solver is to use its own default,
which is documented as 1.0.
rankmu_learning_rate: Learning rate for the rank_mu update
of the covariance matrix of the search distribution.
Leaving this as None means that the CMAES solver is to use
its own default, which is documented as 1.0.
rankone_learning_rate: Learning rate for the rank_one update
of the covariance matrix of the search distribution.
Leaving this as None means that the CMAES solver is to use
its own default, which is documented as 1.0.
stdev_min: Minimum allowed standard deviation of the search
distribution. Leaving this as None means that no such
boundary is to be used.
Can be given as None, as a scalar, or as a 1-dimensional
array.
stdev_max: Maximum allowed standard deviation of the search
distribution. Leaving this as None means that no such
boundary is to be used.
Can be given as None, as a scalar, or as a 1-dimensional
array.
separable: Provide this as True if you would like the problem
to be treated as a separable one. Treating a problem
as separable means to adapt only the diagonal parts
of the covariance matrix and to keep the non-diagonal
parts 0. High dimensional problems result in large
covariance matrices on which operating is computationally
expensive. Therefore, for such high dimensional problems,
setting `separable` as True might be useful.
If, instead, you would like to configure on which
iterations the diagonal parts of the covariance matrix
are to be adapted, then it is recommended to leave
`separable` as False and set a new value for the key
"CMA_diagonal" via `cma_options` (see the official
documentation of pycma for details regarding the
"CMA_diagonal" setting).
obj_index: Objective index according to which evaluation
of the solution will be done.
cma_options: Any other configuration for the CMAES solver
can be passed via the cma_options dictionary.
"""
# Make sure that the cma module is installed
if cma is None:
raise ImportError(f"The class {type(self).__name__} is only available if the package `cma` is installed.")
# Initialize the base class
SearchAlgorithm.__init__(self, problem, center=self._get_center)
# Initialize the population.
self._population: SolutionBatch = self._problem.generate_batch(popsize, empty=True)
# Ensure that the problem is numeric
problem.ensure_numeric()
# Store the objective index
self._obj_index = problem.normalize_obj_index(obj_index)
# If `center_init` is not given, generate an initial solution
# with the help of the problem object.
# Otherwise, use the given initial solution as the starting
# point in the search space.
if center_init is None:
x0 = self._problem.generate_values(1).to("cpu").view(-1).numpy().astype(dtype=float)
else:
x0 = numpy_copy(center_init, dtype=float)
# Store the initial standard deviations
sigma0 = numpy_copy(stdev_init, dtype=float)
# Generate an options dictionary to pass to the cma solver.
inopts = {}
for k, v in cma_options.items():
if isinstance(v, torch.Tensor):
v = numpy_copy(v, dtype=float)
inopts[k] = v
# Remove the number of iterations boundary
if "maxiter" not in inopts:
inopts["maxiter"] = np.inf
# Below is a temporary helper function for safely storing the configuration items.
# This inner function updates the `inopts` variable.
def store_opt(key: str, long_name: str, value: Any, converter: Callable):
# Here, `key` represents the configuration key used by pycma
# `long_name` represents the configuration's long name used by this class
# `value` is the configuration value associated with `key`.
# Declare that this inner function accesses the `inopts` variable.
nonlocal inopts
if value is None:
# If the provided `value` is None, then there is no configuration to store.
# So, we just leave this inner function.
return
if key in inopts:
# If the given `key` already exists within `inopts`, this means that the configuration was specified
# twice: via the keyword argument `cma_options` AND via a keyword argument.
# We raise an error and inform the user about this redundancy.
raise ValueError(
f"The configuration {repr(key)} was redundantly provided"
f" both via the initialization argument {long_name}"
f" and via the cma_options dictionary."
f" {long_name}={repr(value)};"
f" cma_options[{repr(key)}]={repr(inopts[key])}."
)
inopts[key] = converter(value)
# Temporary helper function which makes sure that `x` is a numpy array or a float.
def array_or_float(x):
if is_sequence(x):
return numpy_copy(x)
else:
return float(x)
# Store the cma configuration received through the initialization arguments (and raise error if there is
# redundancy with the cma_options dictionary).
store_opt("popsize", "popsize", popsize, int)
store_opt("CMA_cmean", "center_learning_rate", center_learning_rate, float)
store_opt("CMA_on", "cov_learning_rate", cov_learning_rate, float)
store_opt("CMA_rankmu", "rankmu_learning_rate", rankmu_learning_rate, float)
store_opt("CMA_rankone", "rankone_learning_rate", rankone_learning_rate, float)
store_opt("minstd", "stdev_min", stdev_min, array_or_float)
store_opt("maxstd", "stdev_max", stdev_max, array_or_float)
if separable:
store_opt("CMA_diagonal", "separable", separable, bool)
# If the problem defines lower and upper bounds, pass these into the options dict.
def process_bounds(bounds: RealOrVector) -> np.ndarray:
if bounds is None:
return None
else:
if is_sequence(bounds):
bounds = numpy_copy(bounds)
else:
bounds = np.array(float(bounds)).repeat(self._problem.solution_length)
return bounds
lb = process_bounds(self._problem.lower_bounds)
ub = process_bounds(self._problem.upper_bounds)
register_bounds = False
if lb is not None and ub is None:
ub = np.array(np.inf).repeat(self._problem.solution_length)
register_bounds = True
elif lb is None and ub is not None:
lb = np.array(-(np.inf)).repeat(self._problem.solution_length)
register_bounds = True
elif lb is not None and ub is not None:
register_bounds = True
if register_bounds:
inopts["bounds"] = [lb, ub]
# Generate a random seed using the problem object for the sake of reproducibility.
if "seed" not in inopts:
inopts["seed"] = int(self._problem.make_randint(tuple(), n=(2**32) - 100) + 100)
# Instantiate the CMAEvolutionStrategy with the prepared configuration items.
self._es = cma.CMAEvolutionStrategy(x0, sigma0, inopts)
# Use the SinglePopulationAlgorithmMixin to enable additional status reports regarding the population.
SinglePopulationAlgorithmMixin.__init__(self)
@property
def population(self) -> SolutionBatch:
"""Population generated by the CMA-ES algorithm"""
return self._population
def _step(self):
"""Perform a step of the CMA-ES solver"""
asked = self._es.ask()
self._population.access_values()[:] = torch.as_tensor(
np.asarray(asked), dtype=self._problem.dtype, device=self._population.device
)
self._problem.evaluate(self._population)
scores = numpy_copy(self._population.utility(self._obj_index), dtype=float)
self._es.tell(asked, -1.0 * scores)
def _get_center(self) -> torch.Tensor:
return torch.as_tensor(self._es.result[5], dtype=self._population.dtype, device=self._population.device)
@property
def obj_index(self) -> int:
"""Index of the objective being focused on"""
return self._obj_index
```

###
`obj_index: int`

`property`

`readonly`

¶

Index of the objective being focused on

###
`population: SolutionBatch`

`property`

`readonly`

¶

Population generated by the CMA-ES algorithm

###
`__init__(self, problem, *, stdev_init, popsize=None, center_init=None, center_learning_rate=None, cov_learning_rate=None, rankmu_learning_rate=None, rankone_learning_rate=None, stdev_min=None, stdev_max=None, separable=False, obj_index=None, cma_options={})`

`special`

¶

`__init__(...)`

: Initialize the CMAES solver.

**Parameters:**

Name | Type | Description | Default |
---|---|---|---|

`problem` |
`Problem` |
The problem object which is being worked on. |
required |

`stdev_init` |
`Union[float, Iterable[float], torch.Tensor]` |
Initial standard deviation as a scalar or as a 1-dimensional array. |
required |

`popsize` |
`Optional[int]` |
Population size. Can be specified as an int, or can be left as None to let the CMAES solver decide the population size according to the length of a solution. |
`None` |

`center_init` |
`Union[Iterable[float], torch.Tensor]` |
Initial center point of the search distribution.
Can be given as a SolutionVector or as a 1-D array.
If left as None, an initial center point is generated
with the help of the problem object's |
`None` |

`center_learning_rate` |
`Optional[float]` |
Learning rate for updating the mean of the search distribution. Leaving this as None means that the CMAES solver is to use its own default, which is documented as 1.0. |
`None` |

`cov_learning_rate` |
`Optional[float]` |
Learning rate for updating the covariance matrix of the search distribution. This hyperparameter acts as a common multiplier for rank_one update and rank_mu update of the covariance matrix. Leaving this as None means that the CMAES solver is to use its own default, which is documented as 1.0. |
`None` |

`rankmu_learning_rate` |
`Optional[float]` |
Learning rate for the rank_mu update of the covariance matrix of the search distribution. Leaving this as None means that the CMAES solver is to use its own default, which is documented as 1.0. |
`None` |

`rankone_learning_rate` |
`Optional[float]` |
Learning rate for the rank_one update of the covariance matrix of the search distribution. Leaving this as None means that the CMAES solver is to use its own default, which is documented as 1.0. |
`None` |

`stdev_min` |
`Union[float, numpy.ndarray]` |
Minimum allowed standard deviation of the search distribution. Leaving this as None means that no such boundary is to be used. Can be given as None, as a scalar, or as a 1-dimensional array. |
`None` |

`stdev_max` |
`Union[float, numpy.ndarray]` |
Maximum allowed standard deviation of the search distribution. Leaving this as None means that no such boundary is to be used. Can be given as None, as a scalar, or as a 1-dimensional array. |
`None` |

`separable` |
`bool` |
Provide this as True if you would like the problem
to be treated as a separable one. Treating a problem
as separable means to adapt only the diagonal parts
of the covariance matrix and to keep the non-diagonal
parts 0. High dimensional problems result in large
covariance matrices on which operating is computationally
expensive. Therefore, for such high dimensional problems,
setting |
`False` |

`obj_index` |
`Optional[int]` |
Objective index according to which evaluation of the solution will be done. |
`None` |

`cma_options` |
`dict` |
Any other configuration for the CMAES solver can be passed via the cma_options dictionary. |
`{}` |

## Source code in `evotorch/algorithms/cmaes.py`

```
def __init__(
self,
problem: Problem,
*,
stdev_init: RealOrVector, # sigma0
popsize: Optional[int] = None, # popsize
center_init: Optional[Vector] = None, # x0
center_learning_rate: Optional[float] = None, # CMA_cmean
cov_learning_rate: Optional[float] = None, # CMA_on
rankmu_learning_rate: Optional[float] = None, # CMA_rankmu
rankone_learning_rate: Optional[float] = None, # CMA_rankone
stdev_min: Optional[Union[float, np.ndarray]] = None, # minstd
stdev_max: Optional[Union[float, np.ndarray]] = None, # maxstd
separable: bool = False, # CMA_diagonal
obj_index: Optional[int] = None,
cma_options: dict = {},
):
"""
`__init__(...)`: Initialize the CMAES solver.
Args:
problem: The problem object which is being worked on.
stdev_init: Initial standard deviation as a scalar or
as a 1-dimensional array.
popsize: Population size. Can be specified as an int,
or can be left as None to let the CMAES solver
decide the population size according to the length
of a solution.
center_init: Initial center point of the search distribution.
Can be given as a SolutionVector or as a 1-D array.
If left as None, an initial center point is generated
with the help of the problem object's `generate_values(...)`
method.
center_learning_rate: Learning rate for updating the mean
of the search distribution. Leaving this as None
means that the CMAES solver is to use its own default,
which is documented as 1.0.
cov_learning_rate: Learning rate for updating the covariance
matrix of the search distribution. This hyperparameter
acts as a common multiplier for rank_one update and rank_mu
update of the covariance matrix. Leaving this as None
means that the CMAES solver is to use its own default,
which is documented as 1.0.
rankmu_learning_rate: Learning rate for the rank_mu update
of the covariance matrix of the search distribution.
Leaving this as None means that the CMAES solver is to use
its own default, which is documented as 1.0.
rankone_learning_rate: Learning rate for the rank_one update
of the covariance matrix of the search distribution.
Leaving this as None means that the CMAES solver is to use
its own default, which is documented as 1.0.
stdev_min: Minimum allowed standard deviation of the search
distribution. Leaving this as None means that no such
boundary is to be used.
Can be given as None, as a scalar, or as a 1-dimensional
array.
stdev_max: Maximum allowed standard deviation of the search
distribution. Leaving this as None means that no such
boundary is to be used.
Can be given as None, as a scalar, or as a 1-dimensional
array.
separable: Provide this as True if you would like the problem
to be treated as a separable one. Treating a problem
as separable means to adapt only the diagonal parts
of the covariance matrix and to keep the non-diagonal
parts 0. High dimensional problems result in large
covariance matrices on which operating is computationally
expensive. Therefore, for such high dimensional problems,
setting `separable` as True might be useful.
If, instead, you would like to configure on which
iterations the diagonal parts of the covariance matrix
are to be adapted, then it is recommended to leave
`separable` as False and set a new value for the key
"CMA_diagonal" via `cma_options` (see the official
documentation of pycma for details regarding the
"CMA_diagonal" setting).
obj_index: Objective index according to which evaluation
of the solution will be done.
cma_options: Any other configuration for the CMAES solver
can be passed via the cma_options dictionary.
"""
# Make sure that the cma module is installed
if cma is None:
raise ImportError(f"The class {type(self).__name__} is only available if the package `cma` is installed.")
# Initialize the base class
SearchAlgorithm.__init__(self, problem, center=self._get_center)
# Initialize the population.
self._population: SolutionBatch = self._problem.generate_batch(popsize, empty=True)
# Ensure that the problem is numeric
problem.ensure_numeric()
# Store the objective index
self._obj_index = problem.normalize_obj_index(obj_index)
# If `center_init` is not given, generate an initial solution
# with the help of the problem object.
# Otherwise, use the given initial solution as the starting
# point in the search space.
if center_init is None:
x0 = self._problem.generate_values(1).to("cpu").view(-1).numpy().astype(dtype=float)
else:
x0 = numpy_copy(center_init, dtype=float)
# Store the initial standard deviations
sigma0 = numpy_copy(stdev_init, dtype=float)
# Generate an options dictionary to pass to the cma solver.
inopts = {}
for k, v in cma_options.items():
if isinstance(v, torch.Tensor):
v = numpy_copy(v, dtype=float)
inopts[k] = v
# Remove the number of iterations boundary
if "maxiter" not in inopts:
inopts["maxiter"] = np.inf
# Below is a temporary helper function for safely storing the configuration items.
# This inner function updates the `inopts` variable.
def store_opt(key: str, long_name: str, value: Any, converter: Callable):
# Here, `key` represents the configuration key used by pycma
# `long_name` represents the configuration's long name used by this class
# `value` is the configuration value associated with `key`.
# Declare that this inner function accesses the `inopts` variable.
nonlocal inopts
if value is None:
# If the provided `value` is None, then there is no configuration to store.
# So, we just leave this inner function.
return
if key in inopts:
# If the given `key` already exists within `inopts`, this means that the configuration was specified
# twice: via the keyword argument `cma_options` AND via a keyword argument.
# We raise an error and inform the user about this redundancy.
raise ValueError(
f"The configuration {repr(key)} was redundantly provided"
f" both via the initialization argument {long_name}"
f" and via the cma_options dictionary."
f" {long_name}={repr(value)};"
f" cma_options[{repr(key)}]={repr(inopts[key])}."
)
inopts[key] = converter(value)
# Temporary helper function which makes sure that `x` is a numpy array or a float.
def array_or_float(x):
if is_sequence(x):
return numpy_copy(x)
else:
return float(x)
# Store the cma configuration received through the initialization arguments (and raise error if there is
# redundancy with the cma_options dictionary).
store_opt("popsize", "popsize", popsize, int)
store_opt("CMA_cmean", "center_learning_rate", center_learning_rate, float)
store_opt("CMA_on", "cov_learning_rate", cov_learning_rate, float)
store_opt("CMA_rankmu", "rankmu_learning_rate", rankmu_learning_rate, float)
store_opt("CMA_rankone", "rankone_learning_rate", rankone_learning_rate, float)
store_opt("minstd", "stdev_min", stdev_min, array_or_float)
store_opt("maxstd", "stdev_max", stdev_max, array_or_float)
if separable:
store_opt("CMA_diagonal", "separable", separable, bool)
# If the problem defines lower and upper bounds, pass these into the options dict.
def process_bounds(bounds: RealOrVector) -> np.ndarray:
if bounds is None:
return None
else:
if is_sequence(bounds):
bounds = numpy_copy(bounds)
else:
bounds = np.array(float(bounds)).repeat(self._problem.solution_length)
return bounds
lb = process_bounds(self._problem.lower_bounds)
ub = process_bounds(self._problem.upper_bounds)
register_bounds = False
if lb is not None and ub is None:
ub = np.array(np.inf).repeat(self._problem.solution_length)
register_bounds = True
elif lb is None and ub is not None:
lb = np.array(-(np.inf)).repeat(self._problem.solution_length)
register_bounds = True
elif lb is not None and ub is not None:
register_bounds = True
if register_bounds:
inopts["bounds"] = [lb, ub]
# Generate a random seed using the problem object for the sake of reproducibility.
if "seed" not in inopts:
inopts["seed"] = int(self._problem.make_randint(tuple(), n=(2**32) - 100) + 100)
# Instantiate the CMAEvolutionStrategy with the prepared configuration items.
self._es = cma.CMAEvolutionStrategy(x0, sigma0, inopts)
# Use the SinglePopulationAlgorithmMixin to enable additional status reports regarding the population.
SinglePopulationAlgorithmMixin.__init__(self)
```