Index

Purely functional implementations of optimization algorithms.

Reasoning. PyTorch has a functional API within its namespace torch.func. In addition to allowing one to choose a pure functional programming style, torch.func enables powerful batched operations via torch.func.vmap.

To be able to work with the functional programming style of torch.func, EvoTorch introduces functional implementations of evolutionary search algorithms and optimizers within the namespace evotorch.algorithms.functional. These algorithm implementations are compatible with torch.func.vmap, and therefore they can perform batched evolutionary searches (e.g. they can work on not just a single population, but on batches of populations). Such batched searches can be helpful in the following scenarios:

Scenario 1: Nested optimization. The main optimization problem at hand might have internal optimization problems. Therefore, when the main optimization problem's fitness function is reached, the internal optimization problem will have to be solved for each solution of the main problem. In such a scenario, one might want to use a functional evolutionary search for the inner optimization problem, so that a batch of populations is formed where each batch item represents a separate population associated with a separate solution of the main problem.

Scenario 2: Batched hyperparameter search. If the user is interested in using a search algorithm that has a functional implementation, the user might want to implement a hyperparameter search in such a way that there is a batch of hyperparameters (instead of just a single set of hyperparameters), and the search is performed on a batch of populations. In such a setting, each population within the population batch is associated with a different hyperparameter set within the hyperparameter batch.

Example: cross entropy method. Let us assume that we have the following fitness function, whose output we wish to minimize:

import torch


def f(x: torch.Tensor) -> torch.Tensor:
    assert x.ndim == 2, "Please pass `x` as a 2-dimensional tensor"
    return torch.sum(x**2, dim=-1)

Let us initialize our search from a random point:

solution_length = 1000
center_init = torch.randn(solution_length, dtype=torch.float32) * 10

Now we can initialize our cross entropy method like this:

from evotorch.algorithms.functional import cem, cem_ask, cem_tell

state = cem(
    #
    # Center point of the initial search distribution:
    center_init=center_init,
    #
    #
    # Standard deviation of the initial search distribution:
    stdev_init=10.0,
    #
    #
    # Top half of the population are to be chosen as parents:
    parenthood_ratio=0.5,
    #
    #
    # We wish to minimize the fitnesses:
    objective_sense="min",
    #
    #
    # A standard deviation item is not allowed to change more than
    # 1% of its original value:
    stdev_max_change=0.01,
)

At this point, we have an initial state of our cross entropy method search, stored by the variable state. Now, we can implement a loop and perform multiple generations of evolutionary search like this:

num_generations = 1000

for generation in range(1, 1 + num_generations):
    # Ask for a new population (of size 1000) from cross entropy method
    solutions = cem_ask(state, popsize=1000)

    # At this point, `solutions` is a regular PyTorch tensor, ready to be
    # passed to the function `f`.
    # `solutions` is a 2-dimensional tensor of shape (N, L) where `N`
    # is the number of solutions, and `L` is the length of a solution.
    # Our example fitness function `f` is implemented in such a way that
    # we can pass our 2-dimensional `solutions` tensor into it directly.
    # We will receive `fitnesses` as a 1-dimensional tensor of length `N`.
    fitnesses = f(solutions)

    # Let us report the mean of fitnesses to see the progress
    print("Generation:", generation, "  Mean of fitnesses:", torch.mean(fitnesses))

    # Now, we inform cross entropy method of the latest state of the search,
    # the latest population, and the latest fitnesses, so that it can give us
    # the next state of the search.
    state = cem_tell(state, solutions, fitnesses)

At the end of the evolutionary search (or, actually, at any point), one can analyze the state tuple to get information about the current status of the search distribution. These state tuples are named tuples, and therefore, the data they store are labeled. In the case of cross entropy method, the latest center of the search distribution can be obtained via:

latest_center = state.center

# Note, in the case of pgpe, this would be:
# latest_center = state.optimizer_state.center

Notes on manipulating the evolutionary search. If, at any point of the search, you would like to change a hyperparameter, you can do so by creating a modified copy of your latest state tuple, and pass it to the ask method of your evolutionary search (which, in the case of cross entropy method, is cem_ask). Similarly, if you wish to change the center point of the search, you can pass a modified state tuple containing the new center point to cem_ask.

Notes on batching. In regular non-batched cases, functional search algorithms expect the center_init argument as a 1-dimensional tensor. If center_init is given as a tensor with 2 or more dimensions, the extra leftmost dimensions will be considered as batch dimensions, and therefore the evolutionary search itself will be batched (which means that the ask method of the search algorithm will return a batch of populations). Furthermore, certain hyperparameters can also be given in batches. See the specific documentation of the functional algorithms to see which hyperparameters support batching.

When working with batched populations, it is important to make sure that the fitness function can work with arbitrary amount of dimensions (not just 2 dimensions). One way to implement such fitness functions with the help of the rowwise decorator:

from evotorch.decorators import rowwise


@rowwise
def f(x: torch.Tensor) -> torch.Tensor:
    return torch.sum(x**2)

When decorated with @rowwise, we can implement our function as if the tensor x is a 1-dimensional tensor. If the decorated f receives x not as a vector, but as a matrix, then it will do the same operation on each row of the matrix, in a vectorized manner. If x has 3 or more dimensions, they will be considered as extra batch dimensions, affecting the shape of the resulting tensor.

Example: gradient-based search. This namespace also provides functional implementations of various gradient based optimizers. The reasoning behind the existence of these implementations is two-fold: (i) these optimizers are used by the functional pgpe implementation (for handling the momentum); and (ii) having these optimizers with a similar API allows user to switch back-and-forth between evolutionary and gradient-based search for solving the same problem, hopefully without having to change the code too much.

Let us consider the same fitness function again, in its @rowwise form so that it can work with a single vector or a batch of such vectors:

from evotorch.decorators import rowwise


@rowwise
def f(x: torch.Tensor) -> torch.Tensor:
    return torch.sum(x**2)

To solve this optimization problem using the Adam optimizer, one can do the following:

from evotorch.algorithms.functional import adam, adam_ask, adam_tell
from torch.func import grad

# Prepare an initial search point
solution_length = 1000
center_init = torch.randn(solution_length, dtype=torch.float32) * 10


# Initialize the Adam optimizer
state = adam(
    center_init=center_init,
    center_learning_rate=0.001,
    beta1=0.9,
    beta2=0.999,
    epsilon=1e-8,
)


num_iterations = 1000

for iteration in range(1, 1 + num_iterations):
    # Get the current search point of the Adam search
    center = adam_ask(state)

    # Get the gradient.
    # Negative, because we want to minimize f.
    gradient = -(grad(f)(center))

    # Inform the Adam optimizer of the gradient to follow, and get the next
    # state of the search
    state = adam_tell(state, follow_grad=gradient)


# Store the final solution
final_solution = adam_ask(state)
# or, alternatively:
# final_solution = state.center

Solving a stateful Problem object using functional algorithms. If you wish to solve a stateful Problem using a functional optimization algorithm, you can obtain a callable evaluator out of that Problem object, and then use it for computing the fitnesses. See the following example:

from evotorch import Problem, SolutionBatch
from evotorch.algorithms.functional import cem, cem_ask, cem_tell


class MyProblem(Problem):
    def __init__(self): ...

    def _evaluate_batch(self, batch: SolutionBatch):
        # Stateful batch evaluation code goes here
        ...


# Instantiate the problem
problem = MyProblem()

# Make a callable fitness evaluator
fproblem = problem.make_callable_evaluator()

# Make an initial solution
center_init = torch.randn(problem.solution_length, dtype=torch.float32) * 10


# Prepare a cross entropy method search
state = cem(
    center_init=center_init,
    stdev_init=10.0,
    parenthood_ratio=0.5,
    objective_sense="min",
    stdev_max_change=0.01,
)


num_generations = 1000
for generation in range(1, 1 + num_generations):
    # Get a population
    solutions = cem_ask(state, popsize=1000)

    # Call the evaluator to get the fitnesses
    fitnesses = fproblem(solutions)

    # Let us report the mean of fitnesses to see the progress
    print("Generation:", generation, "  Mean of fitnesses:", torch.mean(fitnesses))

    # Now, we inform cross entropy method of the latest state of the search,
    # the latest population, and the latest fitnesses, so that it can give us
    # the next state of the search.
    state = cem_tell(state, solutions, fitnesses)


# Center of the latest search distribution
latest_center = state.center

adam(*, center_init, center_learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-08)

Initialize an Adam optimizer and return its initial state.

Reference:

Kingma, D. P. and J. Ba (2015).
Adam: A method for stochastic optimization.
In Proceedings of 3rd International Conference on Learning Representations.

Parameters:

Name	Type	Description	Default
center_init	BatchableVector	Starting point for the Adam search. Expected as a PyTorch tensor with at least 1 dimension. If there are 2 or more dimensions, the extra leftmost dimensions are interpreted as batch dimensions.	required
center_learning_rate	BatchableScalar	Learning rate (i.e. the step size) for the Adam updates. Can be a scalar or a multidimensional tensor. If given as a tensor with multiple dimensions, those dimensions will be interpreted as batch dimensions.	0.001
beta1	BatchableScalar	beta1 hyperparameter for the Adam optimizer. Can be a scalar or a multidimensional tensor. If given as a tensor with multiple dimensions, those dimensions will be interpreted as batch dimensions.	0.9
beta2	BatchableScalar	beta2 hyperparameter for the Adam optimizer. Can be a scalar or a multidimensional tensor. If given as a tensor with multiple dimensions, those dimensions will be interpreted as batch dimensions.	0.999
epsilon	BatchableScalar	epsilon hyperparameter for the Adam optimizer. Can be a scalar or a multidimensional tensor. If given as a tensor with multiple dimensions, those dimensions will be interpreted as batch dimensions.	1e-08

Source code in evotorch/algorithms/functional/funcadam.py

def adam(
    *,
    center_init: BatchableVector,
    center_learning_rate: BatchableScalar = 0.001,
    beta1: BatchableScalar = 0.9,
    beta2: BatchableScalar = 0.999,
    epsilon: BatchableScalar = 1e-8,
) -> AdamState:
    """
    Initialize an Adam optimizer and return its initial state.

    Reference:

        Kingma, D. P. and J. Ba (2015).
        Adam: A method for stochastic optimization.
        In Proceedings of 3rd International Conference on Learning Representations.

    Args:
        center_init: Starting point for the Adam search.
            Expected as a PyTorch tensor with at least 1 dimension.
            If there are 2 or more dimensions, the extra leftmost dimensions
            are interpreted as batch dimensions.
        center_learning_rate: Learning rate (i.e. the step size) for the Adam
            updates. Can be a scalar or a multidimensional tensor.
            If given as a tensor with multiple dimensions, those dimensions
            will be interpreted as batch dimensions.
        beta1: beta1 hyperparameter for the Adam optimizer.
            Can be a scalar or a multidimensional tensor.
            If given as a tensor with multiple dimensions, those dimensions
            will be interpreted as batch dimensions.
        beta2: beta2 hyperparameter for the Adam optimizer.
            Can be a scalar or a multidimensional tensor.
            If given as a tensor with multiple dimensions, those dimensions
            will be interpreted as batch dimensions.
        epsilon: epsilon hyperparameter for the Adam optimizer.
            Can be a scalar or a multidimensional tensor.
            If given as a tensor with multiple dimensions, those dimensions
            will be interpreted as batch dimensions.
    Returns:
        A named tuple of type `AdamState`, representing the initial state
        of the Adam optimizer.
    """
    center_init = torch.as_tensor(center_init)
    dtype = center_init.dtype
    device = center_init.device

    def as_tensor(x) -> torch.Tensor:
        return torch.as_tensor(x, dtype=dtype, device=device)

    center_learning_rate = as_tensor(center_learning_rate)
    beta1 = as_tensor(beta1)
    beta2 = as_tensor(beta2)
    epsilon = as_tensor(epsilon)

    m = torch.zeros_like(center_init)
    v = torch.zeros_like(center_init)
    t = torch.zeros(center_init.shape[:-1], dtype=dtype, device=device)

    return AdamState(
        center=center_init,
        center_learning_rate=center_learning_rate,
        beta1=beta1,
        beta2=beta2,
        epsilon=epsilon,
        m=m,
        v=v,
        t=t,
    )

adam_ask(state)

Get the search point stored by the given AdamState.

Parameters:

Name	Type	Description	Default
state	AdamState	The current state of the Adam optimizer.	required

Source code in evotorch/algorithms/functional/funcadam.py

def adam_ask(state: AdamState) -> torch.Tensor:
    """
    Get the search point stored by the given `AdamState`.

    Args:
        state: The current state of the Adam optimizer.
    Returns:
        The search point as a 1-dimensional tensor in the non-batched case,
        or as a multi-dimensional tensor if the Adam search is batched.
    """
    return state.center

adam_tell(state, *, follow_grad)

Tell the Adam optimizer the current gradient to get its next state.

Parameters:

Name	Type	Description	Default
state	AdamState	The current state of the Adam optimizer.	required
follow_grad	BatchableVector	Gradient at the current point of the Adam search. Can be a 1-dimensional tensor in the non-batched case, or a multi-dimensional tensor in the batched case.	required

Source code in evotorch/algorithms/functional/funcadam.py

def adam_tell(state: AdamState, *, follow_grad: BatchableVector) -> AdamState:
    """
    Tell the Adam optimizer the current gradient to get its next state.

    Args:
        state: The current state of the Adam optimizer.
        follow_grad: Gradient at the current point of the Adam search.
            Can be a 1-dimensional tensor in the non-batched case,
            or a multi-dimensional tensor in the batched case.
    Returns:
        The updated state of Adam with the given gradient applied.
    """
    new_center, new_m, new_v, new_t = _adam_step(
        follow_grad,
        state.center,
        state.center_learning_rate,
        state.beta1,
        state.beta2,
        state.epsilon,
        state.m,
        state.v,
        state.t,
    )

    return AdamState(
        center=new_center,
        center_learning_rate=state.center_learning_rate,
        beta1=state.beta1,
        beta2=state.beta2,
        epsilon=state.epsilon,
        m=new_m,
        v=new_v,
        t=new_t,
    )

cem(*, center_init, parenthood_ratio, objective_sense, stdev_init=None, radius_init=None, stdev_min=None, stdev_max=None, stdev_max_change=None)

Get an initial state for the cross entropy method (CEM).

The received initial state, a named tuple of type CEMState, is to be passed to the function cem_ask(...) to receive the solutions belonging to the first generation of the evolutionary search.

References:

Rubinstein, R. (1999). The cross-entropy method for combinatorial
and continuous optimization.
Methodology and computing in applied probability, 1(2), 127-190.

Duan, Y., Chen, X., Houthooft, R., Schulman, J., Abbeel, P. (2016).
Benchmarking deep reinforcement learning for continuous control.
International conference on machine learning. PMLR, 2016.

Parameters:

Name	Type	Description	Default
center_init	BatchableVector	Center (i.e. mean) of the initial search distribution. Expected as a PyTorch tensor with at least 1 dimension. If the given center tensor has more than 1 dimensions, the extra leftmost dimensions will be interpreted as batch dimensions.	required
stdev_init	Optional[Union[float, BatchableVector]]	Standard deviation of the initial search distribution. If this is given as a scalar s, the standard deviation for the search distribution will be interpreted as [s, s, ..., s] whose length is the same with the length of center_init. If this is given as a 1-dimensional tensor, the given tensor will be interpreted as the standard deviation vector. If this is given as a tensor with at least 2 dimensions, the extra leftmost dimension(s) will be interpreted as batch dimensions. If you wish to express the coverage area of the initial search distribution in terms of "radius" instead, you can leave stdev_init as None, and provide a value for the argument radius_init.	None
radius_init	Optional[Union[float, BatchableScalar]]	Radius for the initial search distribution, representing the euclidean norm for the first standard deviation vector. Setting this value as r means that the standard deviation vector will be initialized as a vector [s, s, ..., s] whose norm will be equal to r. In the non-batched case, radius_init is expected as a scalar value. If radius_init is given as a tensor with 1 or more dimensions, those dimensions will be considered as batch dimensions. If you wish to express the coverage are of the initial search distribution in terms of the standard deviation values instead, you can leave radius_init as None, and provide a value for the argument stdev_init.	None
parenthood_ratio	float	Proportion of the solutions that will be chosen as the parents for the next generation. For example, if this is given as 0.5, the top 50% of the solutions will be chosen as parents.	required
objective_sense	str	Expected as a string, either as 'min' or as 'max'. Determines if the goal is to minimize or is to maximize.	required
stdev_min	Optional[Union[float, BatchableVector]]	Minimum allowed standard deviation for the search distribution. Can be given as a scalar or as a tensor with one or more dimensions. When given with at least 2 dimensions, the extra leftmost dimensions will be interpreted as batch dimensions.	None
stdev_max	Optional[Union[float, BatchableVector]]	Maximum allowed standard deviation for the search distribution. Can be given as a scalar or as a tensor with one or more dimensions. When given with at least 2 dimensions, the extra leftmost dimensions will be interpreted as batch dimensions.	None
stdev_max_change	Optional[Union[float, BatchableVector]]	Maximum allowed change for the standard deviation vector. If this is given as a scalar, this scalar will serve as a limiter for the change of the entire standard deviation vector. For example, a scalar value of 0.2 means that the elements of the standard deviation vector cannot change more than the 20% of their original values. If this is given as a vector (i.e. as a 1-dimensional tensor), each element of stdev_max_change will serve as a limiter to its corresponding element within the standard deviation vector. If stdev_max_change is given as a tensor with at least 2 dimensions, the extra leftmost dimension(s) will be interpreted as batch dimensions. If you do not wish to have such a limiter, you can leave this as None.	None

Source code in evotorch/algorithms/functional/funccem.py

def cem(
    *,
    center_init: BatchableVector,
    parenthood_ratio: float,
    objective_sense: str,
    stdev_init: Optional[Union[float, BatchableVector]] = None,
    radius_init: Optional[Union[float, BatchableScalar]] = None,
    stdev_min: Optional[Union[float, BatchableVector]] = None,
    stdev_max: Optional[Union[float, BatchableVector]] = None,
    stdev_max_change: Optional[Union[float, BatchableVector]] = None,
) -> CEMState:
    """
    Get an initial state for the cross entropy method (CEM).

    The received initial state, a named tuple of type `CEMState`, is to be
    passed to the function `cem_ask(...)` to receive the solutions belonging
    to the first generation of the evolutionary search.

    References:

        Rubinstein, R. (1999). The cross-entropy method for combinatorial
        and continuous optimization.
        Methodology and computing in applied probability, 1(2), 127-190.

        Duan, Y., Chen, X., Houthooft, R., Schulman, J., Abbeel, P. (2016).
        Benchmarking deep reinforcement learning for continuous control.
        International conference on machine learning. PMLR, 2016.

    Args:
        center_init: Center (i.e. mean) of the initial search distribution.
            Expected as a PyTorch tensor with at least 1 dimension.
            If the given `center` tensor has more than 1 dimensions, the extra
            leftmost dimensions will be interpreted as batch dimensions.
        stdev_init: Standard deviation of the initial search distribution.
            If this is given as a scalar `s`, the standard deviation for the
            search distribution will be interpreted as `[s, s, ..., s]` whose
            length is the same with the length of `center_init`.
            If this is given as a 1-dimensional tensor, the given tensor will
            be interpreted as the standard deviation vector.
            If this is given as a tensor with at least 2 dimensions, the extra
            leftmost dimension(s) will be interpreted as batch dimensions.
            If you wish to express the coverage area of the initial search
            distribution in terms of "radius" instead, you can leave
            `stdev_init` as None, and provide a value for the argument
            `radius_init`.
        radius_init: Radius for the initial search distribution, representing
            the euclidean norm for the first standard deviation vector.
            Setting this value as `r` means that the standard deviation
            vector will be initialized as a vector `[s, s, ..., s]`
            whose norm will be equal to `r`. In the non-batched case,
            `radius_init` is expected as a scalar value.
            If `radius_init` is given as a tensor with 1 or more
            dimensions, those dimensions will be considered as batch
            dimensions. If you wish to express the coverage are of the initial
            search distribution in terms of the standard deviation values
            instead, you can leave `radius_init` as None, and provide a value
            for the argument `stdev_init`.
        parenthood_ratio: Proportion of the solutions that will be chosen as
            the parents for the next generation. For example, if this is
            given as 0.5, the top 50% of the solutions will be chosen as
            parents.
        objective_sense: Expected as a string, either as 'min' or as 'max'.
            Determines if the goal is to minimize or is to maximize.
        stdev_min: Minimum allowed standard deviation for the search
            distribution. Can be given as a scalar or as a tensor with one or
            more dimensions. When given with at least 2 dimensions, the extra
            leftmost dimensions will be interpreted as batch dimensions.
        stdev_max: Maximum allowed standard deviation for the search
            distribution. Can be given as a scalar or as a tensor with one or
            more dimensions. When given with at least 2 dimensions, the extra
            leftmost dimensions will be interpreted as batch dimensions.
        stdev_max_change: Maximum allowed change for the standard deviation
            vector. If this is given as a scalar, this scalar will serve as a
            limiter for the change of the entire standard deviation vector.
            For example, a scalar value of 0.2 means that the elements of the
            standard deviation vector cannot change more than the 20% of their
            original values. If this is given as a vector (i.e. as a
            1-dimensional tensor), each element of `stdev_max_change` will
            serve as a limiter to its corresponding element within the standard
            deviation vector. If `stdev_max_change` is given as a tensor with
            at least 2 dimensions, the extra leftmost dimension(s) will be
            interpreted as batch dimensions.
            If you do not wish to have such a limiter, you can leave this as
            None.
    Returns:
        A named tuple, of type `CEMState`, storing the hyperparameters and the
        initial state of the cross entropy method.
    """
    from .misc import _get_stdev_init

    center_init = torch.as_tensor(center_init)
    if center_init.ndim < 1:
        raise ValueError(
            "The center of the search distribution for the functional CEM was expected"
            " as a tensor with at least 1 dimension."
            f" However, the encountered `center_init` is {center_init}, of shape {center_init.shape}."
        )

    solution_length = center_init.shape[-1]
    if solution_length == 0:
        raise ValueError("Solution length cannot be 0")

    stdev_init = _get_stdev_init(center_init=center_init, stdev_init=stdev_init, radius_init=radius_init)

    device = center_init.device
    dtype = center_init.dtype

    def as_vector_like_center(x: Iterable, vector_name: str) -> torch.Tensor:
        x = torch.as_tensor(x, dtype=dtype, device=device)
        if x.ndim == 0:
            x = x.repeat(solution_length)
        else:
            if x.shape[-1] != solution_length:
                raise ValueError(
                    f"`{vector_name}` has an incompatible length."
                    f" The length of `{vector_name}`: {x.shape[-1]},"
                    f" but the solution length implied by the provided `center_init` is {solution_length}."
                )
        return x

    if stdev_min is None:
        stdev_min = 0.0
    stdev_min = as_vector_like_center(stdev_min, "stdev_min")

    if stdev_max is None:
        stdev_max = float("inf")
    stdev_max = as_vector_like_center(stdev_max, "stdev_max")

    if stdev_max_change is None:
        stdev_max_change = float("inf")
    stdev_max_change = as_vector_like_center(stdev_max_change, "stdev_max_change")
    parenthood_ratio = float(parenthood_ratio)

    if objective_sense == "min":
        maximize = False
    elif objective_sense == "max":
        maximize = True
    else:
        raise ValueError(
            f"`objective_sense` was expected as 'min' or 'max', but it was received as {repr(objective_sense)}"
        )

    return CEMState(
        center=center_init,
        stdev=stdev_init,
        stdev_min=stdev_min,
        stdev_max=stdev_max,
        stdev_max_change=stdev_max_change,
        parenthood_ratio=parenthood_ratio,
        maximize=maximize,
    )

cem_ask(state, *, popsize)

Obtain a population from cross entropy method, given the state.

Parameters:

Name	Type	Description	Default
state	CEMState	The current state of the cross entropy method search.	required
popsize	int	Number of solutions to be generated for the requested population.	required

Source code in evotorch/algorithms/functional/funccem.py

def cem_ask(state: CEMState, *, popsize: int) -> torch.Tensor:
    """
    Obtain a population from cross entropy method, given the state.

    Args:
        state: The current state of the cross entropy method search.
        popsize: Number of solutions to be generated for the requested
            population.
    Returns:
        Population, as a tensor of at least 2 dimensions.
    """
    return _cem_ask(state.center, state.stdev, state.parenthood_ratio, popsize)

cem_tell(state, values, evals)

Given the old state and the evals (fitnesses), obtain the next state.

From this state tuple, the center point of the search distribution can be obtained via the field .center.

Parameters:

Name	Type	Description	Default
state	CEMState	The old state of the cross entropy method search.	required
values	Tensor	The most recent population, as a PyTorch tensor.	required
evals	Tensor	Evaluation results (i.e. fitnesses) for the solutions expressed by values. For example, if values is shaped (N, L), this means that there are N solutions (of length L). So, evals is expected as a 1-dimensional tensor of length N, where evals[i] expresses the fitness of the solution values[i, :]. If values is shaped (B, N, L), then there is also a batch dimension, so, evals is expected as a 2-dimensional tensor of shape (B, N).	required

Source code in evotorch/algorithms/functional/funccem.py

def cem_tell(state: CEMState, values: torch.Tensor, evals: torch.Tensor) -> CEMState:
    """
    Given the old state and the evals (fitnesses), obtain the next state.

    From this state tuple, the center point of the search distribution can be
    obtained via the field `.center`.

    Args:
        state: The old state of the cross entropy method search.
        values: The most recent population, as a PyTorch tensor.
        evals: Evaluation results (i.e. fitnesses) for the solutions expressed
            by `values`. For example, if `values` is shaped `(N, L)`, this means
            that there are `N` solutions (of length `L`). So, `evals` is
            expected as a 1-dimensional tensor of length `N`, where `evals[i]`
            expresses the fitness of the solution `values[i, :]`.
            If `values` is shaped `(B, N, L)`, then there is also a batch
            dimension, so, `evals` is expected as a 2-dimensional tensor of
            shape `(B, N)`.
    Returns:
        The new state of the cross entropy method search.
    """
    new_center, new_stdev = _cem_tell(
        state.stdev_min,
        state.stdev_max,
        state.stdev_max_change,
        state.parenthood_ratio,
        state.maximize,
        state.center,
        state.stdev,
        values,
        evals,
    )
    return CEMState(
        center=new_center,
        stdev=new_stdev,
        stdev_min=state.stdev_min,
        stdev_max=state.stdev_max,
        stdev_max_change=state.stdev_max_change,
        parenthood_ratio=state.parenthood_ratio,
        maximize=state.maximize,
    )

clipup(*, center_init, momentum=0.9, center_learning_rate=None, max_speed=None)

Initialize the ClipUp optimizer and return its initial state.

Reference:

Toklu, N. E., Liskowski, P., & Srivastava, R. K. (2020, September).
ClipUp: A Simple and Powerful Optimizer for Distribution-Based Policy Evolution.
In International Conference on Parallel Problem Solving from Nature (pp. 515-527).
Springer, Cham.

Parameters:

Name	Type	Description	Default
center_init	BatchableVector	Starting point for the ClipUp search. Expected as a PyTorch tensor with at least 1 dimension. If there are 2 or more dimensions, the extra leftmost dimensions are interpreted as batch dimensions.	required
center_learning_rate	Optional[BatchableScalar]	Learning rate (i.e. the step size) for the ClipUp updates. Can be a scalar or a multidimensional tensor. If given as a tensor with multiple dimensions, those dimensions will be interpreted as batch dimensions.	None
max_speed	Optional[BatchableScalar]	Maximum speed, expected as a scalar. The euclidean norm of the velocity (i.e. of the update vector) is not allowed to exceed max_speed. If given as a tensor with multiple dimensions, those dimensions will be interpreted as batch dimensions.	None

Source code in evotorch/algorithms/functional/funcclipup.py

def clipup(
    *,
    center_init: BatchableVector,
    momentum: BatchableScalar = 0.9,
    center_learning_rate: Optional[BatchableScalar] = None,
    max_speed: Optional[BatchableScalar] = None,
) -> ClipUpState:
    """
    Initialize the ClipUp optimizer and return its initial state.

    Reference:

        Toklu, N. E., Liskowski, P., & Srivastava, R. K. (2020, September).
        ClipUp: A Simple and Powerful Optimizer for Distribution-Based Policy Evolution.
        In International Conference on Parallel Problem Solving from Nature (pp. 515-527).
        Springer, Cham.

    Args:
        center_init: Starting point for the ClipUp search.
            Expected as a PyTorch tensor with at least 1 dimension.
            If there are 2 or more dimensions, the extra leftmost dimensions
            are interpreted as batch dimensions.
        center_learning_rate: Learning rate (i.e. the step size) for the ClipUp
            updates. Can be a scalar or a multidimensional tensor.
            If given as a tensor with multiple dimensions, those dimensions
            will be interpreted as batch dimensions.
        max_speed: Maximum speed, expected as a scalar. The euclidean norm
            of the velocity (i.e. of the update vector) is not allowed to
            exceed `max_speed`.
            If given as a tensor with multiple dimensions, those dimensions
            will be interpreted as batch dimensions.
    """
    center_init = torch.as_tensor(center_init)
    dtype = center_init.dtype
    device = center_init.device

    def as_tensor(x) -> torch.Tensor:
        return torch.as_tensor(x, dtype=dtype, device=device)

    if (center_learning_rate is None) and (max_speed is None):
        raise ValueError("Both `center_learning_rate` and `max_speed` is missing. At least one of them is needed.")
    elif (center_learning_rate is not None) and (max_speed is None):
        center_learning_rate = as_tensor(center_learning_rate)
        max_speed = center_learning_rate * 2.0
    elif (center_learning_rate is None) and (max_speed is not None):
        max_speed = as_tensor(max_speed)
        center_learning_rate = max_speed / 2.0
    else:
        center_learning_rate = as_tensor(center_learning_rate)
        max_speed = as_tensor(max_speed)

    velocity = torch.zeros_like(center_init)
    momentum = as_tensor(momentum)

    return ClipUpState(
        center=center_init,
        velocity=velocity,
        center_learning_rate=center_learning_rate,
        momentum=momentum,
        max_speed=max_speed,
    )

clipup_ask(state)

Get the search point stored by the given ClipUpState.

Parameters:

Name	Type	Description	Default
state	ClipUpState	The current state of the ClipUp optimizer.	required

Source code in evotorch/algorithms/functional/funcclipup.py

def clipup_ask(state: ClipUpState) -> torch.Tensor:
    """
    Get the search point stored by the given `ClipUpState`.

    Args:
        state: The current state of the ClipUp optimizer.
    Returns:
        The search point as a 1-dimensional tensor in the non-batched case,
        or as a multi-dimensional tensor if the ClipUp search is batched.
    """
    return state.center

clipup_tell(state, *, follow_grad)

Tell the ClipUp optimizer the current gradient to get its next state.

Parameters:

Name	Type	Description	Default
state	ClipUpState	The current state of the ClipUp optimizer.	required
follow_grad	BatchableVector	Gradient at the current point of the Adam search. Can be a 1-dimensional tensor in the non-batched case, or a multi-dimensional tensor in the batched case.	required

Source code in evotorch/algorithms/functional/funcclipup.py

def clipup_tell(state: ClipUpState, *, follow_grad: BatchableVector) -> ClipUpState:
    """
    Tell the ClipUp optimizer the current gradient to get its next state.

    Args:
        state: The current state of the ClipUp optimizer.
        follow_grad: Gradient at the current point of the Adam search.
            Can be a 1-dimensional tensor in the non-batched case,
            or a multi-dimensional tensor in the batched case.
    Returns:
        The updated state of ClipUp with the given gradient applied.
    """
    velocity, center = _clipup_step(
        follow_grad,
        state.center,
        state.velocity,
        state.center_learning_rate,
        state.momentum,
        state.max_speed,
    )

    return ClipUpState(
        center=center,
        velocity=velocity,
        center_learning_rate=state.center_learning_rate,
        momentum=state.momentum,
        max_speed=state.max_speed,
    )

pgpe(*, center_init, center_learning_rate, stdev_learning_rate, objective_sense, ranking_method='centered', optimizer='clipup', optimizer_config=None, stdev_init=None, radius_init=None, stdev_min=None, stdev_max=None, stdev_max_change=0.2, symmetric=True)

Get an initial state for the PGPE algorithm.

The received initial state, a named tuple of type PGPEState, is to be passed to the function pgpe_ask(...) to receive the solutions belonging to the first generation of the evolutionary search.

Inspired by the PGPE implementations used in the studies of Ha (2017, 2019), and by the evolution strategy variant of Salimans et al. (2017), this PGPE implementation uses 0-centered ranking by default. The default optimizer for this PGPE implementation is ClipUp (Toklu et al., 2020).

References:

Frank Sehnke, Christian Osendorfer, Thomas Ruckstiess,
Alex Graves, Jan Peters, Jurgen Schmidhuber (2010).
Parameter-exploring Policy Gradients.
Neural Networks 23(4), 551-559.

David Ha (2017). Evolving Stable Strategies.
<http://blog.otoro.net/2017/11/12/evolving-stable-strategies/>

Salimans, T., Ho, J., Chen, X., Sidor, S. and Sutskever, I. (2017).
Evolution Strategies as a Scalable Alternative to
Reinforcement Learning.

David Ha (2019). Reinforcement Learning for Improving Agent Design.
Artificial life 25 (4), 352-365.

Toklu, N.E., Liskowski, P., Srivastava, R.K. (2020).
ClipUp: A Simple and Powerful Optimizer
for Distribution-based Policy Evolution.
Parallel Problem Solving from Nature (PPSN 2020).

Parameters:

Name	Type	Description	Default
center_init	BatchableVector	Center (i.e. mean) of the initial search distribution. Expected as a PyTorch tensor with at least 1 dimension. If the given center tensor has more than 1 dimensions, the extra leftmost dimensions will be interpreted as batch dimensions.	required
center_learning_rate	BatchableScalar	Learning rate for when updating the center of the search distribution. For normal cases, this is expected as a scalar. If given as an n-dimensional tensor (where n>0), the extra dimensions will be considered as batch dimensions.	required
stdev_learning_rate	BatchableScalar	Learning rate for when updating the standard deviation of the search distribution. For normal cases, this is expected as a scalar. If given as an n-dimensional tensor (where n>0), the extra dimensions will be considered as batch dimensions.	required
objective_sense	str	Expected as a string, either as 'min' or as 'max'. Determines if the goal is to minimize or is to maximize.	required
ranking_method	str	Determines how the fitnesses will be ranked before computing the gradients. Among the choices are "centered" (a linear ranking where the worst solution gets the rank -0.5 and the best solution gets the rank +0.5), "linear" (a linear ranking where the worst solution gets the rank 0 and the best solution gets the rank 1), "nes" (the ranking method that is used by the natural evolution strategies), and "raw" (no ranking).	'centered'
optimizer	Union[str, tuple]	Functional optimizer to use when updating the center of the search distribution. The functional optimizer can be expressed via a string, or via a tuple. If given as string, the valid choices are: "clipup" (for the ClipUp optimizer), "adam" (for the Adam optimizer), "sgd" (for regular gradient ascent/descent). If given as a tuple, the tuple should be in the form (optim, optim_ask, optim_tell), where the objects optim, optim_ask, and optim_tell are the functions for initializing the optimizer, asking (for the current search point), and telling (the gradient to follow). The function optim should expect keyword arguments for its hyperparameters, and should return a state tuple of the optimizer. The function optim_ask should expect the state tuple of the optimizer, and should return the current search point as a tensor. The function optim_tell should expect the state tuple of the optimizer as a positional argument, and the gradient via the keyword argument follow_grad.	'clipup'
optimizer_config	Optional[dict]	Optionally a dictionary, containing the hyperparameters for the optimizer.	None
stdev_init	Optional[Union[float, BatchableVector]]	Standard deviation of the initial search distribution. If this is given as a scalar s, the standard deviation for the search distribution will be interpreted as [s, s, ..., s] whose length is the same with the length of center_init. If this is given as a 1-dimensional tensor, the given tensor will be interpreted as the standard deviation vector. If this is given as a tensor with at least 2 dimensions, the extra leftmost dimension(s) will be interpreted as batch dimensions. If you wish to express the coverage area of the initial search distribution in terms of "radius" instead, you can leave stdev_init as None, and provide a value for the argument radius_init.	None
radius_init	Optional[Union[float, BatchableScalar]]	Radius for the initial search distribution, representing the euclidean norm for the first standard deviation vector. Setting this value as r means that the standard deviation vector will be initialized as a vector [s, s, ..., s] whose norm will be equal to r. In the non-batched case, radius_init is expected as a scalar value. If radius_init is given as a tensor with 1 or more dimensions, those dimensions will be considered as batch dimensions. If you wish to express the coverage are of the initial search distribution in terms of the standard deviation values instead, you can leave radius_init as None, and provide a value for the argument stdev_init.	None
stdev_min	Optional[Union[float, BatchableVector]]	Minimum allowed standard deviation for the search distribution. Can be given as a scalar or as a tensor with one or more dimensions. When given with at least 2 dimensions, the extra leftmost dimensions will be interpreted as batch dimensions.	None
stdev_max	Optional[Union[float, BatchableVector]]	Maximum allowed standard deviation for the search distribution. Can be given as a scalar or as a tensor with one or more dimensions. When given with at least 2 dimensions, the extra leftmost dimensions will be interpreted as batch dimensions.	None
stdev_max_change	Optional[Union[float, BatchableVector]]	Maximum allowed change for the standard deviation vector. If this is given as a scalar, this scalar will serve as a limiter for the change of the entire standard deviation vector. For example, a scalar value of 0.2 means that the elements of the standard deviation vector cannot change more than the 20% of their original values. If this is given as a vector (i.e. as a 1-dimensional tensor), each element of stdev_max_change will serve as a limiter to its corresponding element within the standard deviation vector. If stdev_max_change is given as a tensor with at least 2 dimensions, the extra leftmost dimension(s) will be interpreted as batch dimensions. If you do not wish to have such a limiter, you can leave this as None.	0.2
symmetric	bool	Whether or not symmetric (i.e. antithetic) sampling will be done while generating a new population.	True

Source code in evotorch/algorithms/functional/funcpgpe.py

def pgpe(
    *,
    center_init: BatchableVector,
    center_learning_rate: BatchableScalar,
    stdev_learning_rate: BatchableScalar,
    objective_sense: str,
    ranking_method: str = "centered",
    optimizer: Union[str, tuple] = "clipup",  # or "adam" or "sgd"
    optimizer_config: Optional[dict] = None,
    stdev_init: Optional[Union[float, BatchableVector]] = None,
    radius_init: Optional[Union[float, BatchableScalar]] = None,
    stdev_min: Optional[Union[float, BatchableVector]] = None,
    stdev_max: Optional[Union[float, BatchableVector]] = None,
    stdev_max_change: Optional[Union[float, BatchableVector]] = 0.2,
    symmetric: bool = True,
) -> PGPEState:
    """
    Get an initial state for the PGPE algorithm.

    The received initial state, a named tuple of type `PGPEState`, is to be
    passed to the function `pgpe_ask(...)` to receive the solutions belonging
    to the first generation of the evolutionary search.

    Inspired by the PGPE implementations used in the studies
    of Ha (2017, 2019), and by the evolution strategy variant of
    Salimans et al. (2017), this PGPE implementation uses 0-centered
    ranking by default.
    The default optimizer for this PGPE implementation is ClipUp
    (Toklu et al., 2020).

    References:

        Frank Sehnke, Christian Osendorfer, Thomas Ruckstiess,
        Alex Graves, Jan Peters, Jurgen Schmidhuber (2010).
        Parameter-exploring Policy Gradients.
        Neural Networks 23(4), 551-559.

        David Ha (2017). Evolving Stable Strategies.
        <http://blog.otoro.net/2017/11/12/evolving-stable-strategies/>

        Salimans, T., Ho, J., Chen, X., Sidor, S. and Sutskever, I. (2017).
        Evolution Strategies as a Scalable Alternative to
        Reinforcement Learning.

        David Ha (2019). Reinforcement Learning for Improving Agent Design.
        Artificial life 25 (4), 352-365.

        Toklu, N.E., Liskowski, P., Srivastava, R.K. (2020).
        ClipUp: A Simple and Powerful Optimizer
        for Distribution-based Policy Evolution.
        Parallel Problem Solving from Nature (PPSN 2020).

    Args:
        center_init: Center (i.e. mean) of the initial search distribution.
            Expected as a PyTorch tensor with at least 1 dimension.
            If the given `center` tensor has more than 1 dimensions, the extra
            leftmost dimensions will be interpreted as batch dimensions.
        center_learning_rate: Learning rate for when updating the center of the
            search distribution.
            For normal cases, this is expected as a scalar. If given as an
            n-dimensional tensor (where n>0), the extra dimensions will be
            considered as batch dimensions.
        stdev_learning_rate: Learning rate for when updating the standard
            deviation of the search distribution.
            For normal cases, this is expected as a scalar. If given as an
            n-dimensional tensor (where n>0), the extra dimensions will be
            considered as batch dimensions.
        objective_sense: Expected as a string, either as 'min' or as 'max'.
            Determines if the goal is to minimize or is to maximize.
        ranking_method: Determines how the fitnesses will be ranked before
            computing the gradients. Among the choices are
            "centered" (a linear ranking where the worst solution gets the rank
            -0.5 and the best solution gets the rank +0.5),
            "linear" (a linear ranking where the worst solution gets the rank
            0 and the best solution gets the rank 1),
            "nes" (the ranking method that is used by the natural evolution
            strategies), and
            "raw" (no ranking).
        optimizer: Functional optimizer to use when updating the center of the
            search distribution. The functional optimizer can be expressed via
            a string, or via a tuple.
            If given as string, the valid choices are:
            "clipup" (for the ClipUp optimizer),
            "adam" (for the Adam optimizer),
            "sgd" (for regular gradient ascent/descent).
            If given as a tuple, the tuple should be in the form
            `(optim, optim_ask, optim_tell)`, where the objects
            `optim`, `optim_ask`, and `optim_tell` are the functions for
            initializing the optimizer, asking (for the current search point),
            and telling (the gradient to follow).
            The function `optim` should expect keyword arguments for its
            hyperparameters, and should return a state tuple of the optimizer.
            The function `optim_ask` should expect the state tuple of the
            optimizer, and should return the current search point as a tensor.
            The function `optim_tell` should expect the state tuple of the
            optimizer as a positional argument, and the gradient via the
            keyword argument `follow_grad`.
        optimizer_config: Optionally a dictionary, containing the
            hyperparameters for the optimizer.
        stdev_init: Standard deviation of the initial search distribution.
            If this is given as a scalar `s`, the standard deviation for the
            search distribution will be interpreted as `[s, s, ..., s]` whose
            length is the same with the length of `center_init`.
            If this is given as a 1-dimensional tensor, the given tensor will
            be interpreted as the standard deviation vector.
            If this is given as a tensor with at least 2 dimensions, the extra
            leftmost dimension(s) will be interpreted as batch dimensions.
            If you wish to express the coverage area of the initial search
            distribution in terms of "radius" instead, you can leave
            `stdev_init` as None, and provide a value for the argument
            `radius_init`.
        radius_init: Radius for the initial search distribution, representing
            the euclidean norm for the first standard deviation vector.
            Setting this value as `r` means that the standard deviation
            vector will be initialized as a vector `[s, s, ..., s]`
            whose norm will be equal to `r`. In the non-batched case,
            `radius_init` is expected as a scalar value.
            If `radius_init` is given as a tensor with 1 or more
            dimensions, those dimensions will be considered as batch
            dimensions. If you wish to express the coverage are of the initial
            search distribution in terms of the standard deviation values
            instead, you can leave `radius_init` as None, and provide a value
            for the argument `stdev_init`.
        stdev_min: Minimum allowed standard deviation for the search
            distribution. Can be given as a scalar or as a tensor with one or
            more dimensions. When given with at least 2 dimensions, the extra
            leftmost dimensions will be interpreted as batch dimensions.
        stdev_max: Maximum allowed standard deviation for the search
            distribution. Can be given as a scalar or as a tensor with one or
            more dimensions. When given with at least 2 dimensions, the extra
            leftmost dimensions will be interpreted as batch dimensions.
        stdev_max_change: Maximum allowed change for the standard deviation
            vector. If this is given as a scalar, this scalar will serve as a
            limiter for the change of the entire standard deviation vector.
            For example, a scalar value of 0.2 means that the elements of the
            standard deviation vector cannot change more than the 20% of their
            original values. If this is given as a vector (i.e. as a
            1-dimensional tensor), each element of `stdev_max_change` will
            serve as a limiter to its corresponding element within the standard
            deviation vector. If `stdev_max_change` is given as a tensor with
            at least 2 dimensions, the extra leftmost dimension(s) will be
            interpreted as batch dimensions.
            If you do not wish to have such a limiter, you can leave this as
            None.
        symmetric: Whether or not symmetric (i.e. antithetic) sampling will be
            done while generating a new population.
    Returns:
        A named tuple, of type `CEMState`, storing the hyperparameters and the
        initial state of the cross entropy method.
    """
    from .misc import _get_stdev_init, get_functional_optimizer

    center_init = torch.as_tensor(center_init)
    if center_init.ndim < 1:
        raise ValueError(
            "The center of the search distribution for the functional PGPE was expected"
            " as a tensor with at least 1 dimension."
            f" However, the encountered `center` is {center_init}, of shape {center_init.shape}."
        )

    solution_length = center_init.shape[-1]
    if solution_length == 0:
        raise ValueError("Solution length cannot be 0")

    stdev_init = _get_stdev_init(center_init=center_init, stdev_init=stdev_init, radius_init=radius_init)

    device = center_init.device
    dtype = center_init.dtype

    def as_tensor(x) -> torch.Tensor:
        return torch.as_tensor(x, dtype=dtype, device=device)

    def as_vector_like_center(x: Iterable, vector_name: str) -> torch.Tensor:
        x = as_tensor(x)
        if x.ndim == 0:
            x = x.repeat(solution_length)
        else:
            if x.shape[-1] != solution_length:
                raise ValueError(
                    f"`{vector_name}` has an incompatible length."
                    f" The length of `{vector_name}`: {x.shape[-1]},"
                    f" but the solution length implied by the provided `center_init` is {solution_length}."
                )
        return x

    center_learning_rate = as_tensor(center_learning_rate)
    stdev_learning_rate = as_tensor(stdev_learning_rate)

    if objective_sense == "min":
        maximize = False
    elif objective_sense == "max":
        maximize = True
    else:
        raise ValueError(
            f"`objective_sense` was expected as 'min' or 'max', but it was received as {repr(objective_sense)}"
        )

    ranking_method = str(ranking_method)

    if stdev_min is None:
        stdev_min = 0.0
    stdev_min = as_vector_like_center(stdev_min, "stdev_min")

    if stdev_max is None:
        stdev_max = float("inf")
    stdev_max = as_vector_like_center(stdev_max, "stdev_max")

    if stdev_max_change is None:
        stdev_max_change = float("inf")
    stdev_max_change = as_vector_like_center(stdev_max_change, "stdev_max_change")

    if optimizer_config is None:
        optimizer_config = {}
    optimizer_init_func, _, _ = get_functional_optimizer(optimizer)
    optimizer_state = optimizer_init_func(
        center_init=center_init, center_learning_rate=center_learning_rate, **optimizer_config
    )

    symmetric = bool(symmetric)

    return PGPEState(
        optimizer=optimizer,
        optimizer_state=optimizer_state,
        stdev=stdev_init,
        stdev_learning_rate=stdev_learning_rate,
        stdev_min=stdev_min,
        stdev_max=stdev_max,
        stdev_max_change=stdev_max_change,
        ranking_method=ranking_method,
        maximize=maximize,
        symmetric=symmetric,
    )

pgpe_ask(state, *, popsize)

Obtain a population from the PGPE algorithm.

Parameters:

Name	Type	Description	Default
state	PGPEState	The current state of PGPE.	required
popsize	int	Number of solutions to be generated for the requested population.	required

Source code in evotorch/algorithms/functional/funcpgpe.py

def pgpe_ask(state: PGPEState, *, popsize: int) -> torch.Tensor:
    """
    Obtain a population from the PGPE algorithm.

    Args:
        state: The current state of PGPE.
        popsize: Number of solutions to be generated for the requested
            population.
    Returns:
        Population, as a tensor of at least 2 dimensions.
    """
    from .misc import get_functional_optimizer

    _, optimizer_ask, _ = get_functional_optimizer(state.optimizer)
    center = optimizer_ask(state.optimizer_state)
    stdev = state.stdev
    sample_func = _symmetic_sample if state.symmetric else _nonsymmetric_sample
    return sample_func(popsize, mu=center, sigma=stdev)

pgpe_tell(state, values, evals)

Given the old state and the evals (fitnesses), obtain the next state.

From this state tuple, the center point of the search distribution can be obtained via the field .optimizer_state.center.

Parameters:

Name	Type	Description	Default
state	PGPEState	The old state of the cross entropy method search.	required
values	Tensor	The most recent population, as a PyTorch tensor.	required
evals	Tensor	Evaluation results (i.e. fitnesses) for the solutions expressed by values. For example, if values is shaped (N, L), this means that there are N solutions (of length L). So, evals is expected as a 1-dimensional tensor of length N, where evals[i] expresses the fitness of the solution values[i, :]. If values is shaped (B, N, L), then there is also a batch dimension, so, evals is expected as a 2-dimensional tensor of shape (B, N).	required

Source code in evotorch/algorithms/functional/funcpgpe.py

def pgpe_tell(state: PGPEState, values: torch.Tensor, evals: torch.Tensor) -> PGPEState:
    """
    Given the old state and the evals (fitnesses), obtain the next state.

    From this state tuple, the center point of the search distribution can be
    obtained via the field `.optimizer_state.center`.

    Args:
        state: The old state of the cross entropy method search.
        values: The most recent population, as a PyTorch tensor.
        evals: Evaluation results (i.e. fitnesses) for the solutions expressed
            by `values`. For example, if `values` is shaped `(N, L)`, this means
            that there are `N` solutions (of length `L`). So, `evals` is
            expected as a 1-dimensional tensor of length `N`, where `evals[i]`
            expresses the fitness of the solution `values[i, :]`.
            If `values` is shaped `(B, N, L)`, then there is also a batch
            dimension, so, `evals` is expected as a 2-dimensional tensor of
            shape `(B, N)`.
    Returns:
        The new state of PGPE.
    """
    from .misc import get_functional_optimizer

    _, optimizer_ask, optimizer_tell = get_functional_optimizer(state.optimizer)

    grad_func = _symmetric_grad if state.symmetric else _nonsymmetric_grad
    objective_sense = "max" if state.maximize else "min"
    grads = grad_func(
        values,
        evals,
        mu=optimizer_ask(state.optimizer_state),
        sigma=state.stdev,
        objective_sense=objective_sense,
        ranking_method=state.ranking_method,
    )

    new_optimizer_state = optimizer_tell(state.optimizer_state, follow_grad=grads["mu"])

    target_stdev = _follow_stdev_grad(state.stdev, state.stdev_learning_rate, grads["sigma"])
    new_stdev = modify_vector(
        state.stdev, target_stdev, lb=state.stdev_min, ub=state.stdev_max, max_change=state.stdev_max_change
    )

    return PGPEState(
        optimizer=state.optimizer,
        optimizer_state=new_optimizer_state,
        stdev=new_stdev,
        stdev_learning_rate=state.stdev_learning_rate,
        stdev_min=state.stdev_min,
        stdev_max=state.stdev_max,
        stdev_max_change=state.stdev_max_change,
        ranking_method=state.ranking_method,
        maximize=state.maximize,
        symmetric=state.symmetric,
    )

sgd(*, center_init, center_learning_rate, momentum=None)

Initialize the gradient ascent/descent search and get its initial state.

Reference regarding the momentum behavior:

Polyak, B. T. (1964).
Some methods of speeding up the convergence of iteration methods.
USSR Computational Mathematics and Mathematical Physics, 4(5):1–17.

Parameters:

Name	Type	Description	Default
center_init	BatchableVector	Starting point for the gradient ascent/descent. Expected as a PyTorch tensor with at least 1 dimension. If there are 2 or more dimensions, the extra leftmost dimensions are interpreted as batch dimensions.	required
center_learning_rate	BatchableScalar	Learning rate (i.e. the step size) for gradient ascent/descent. Can be a scalar or a multidimensional tensor. If given as a tensor with multiple dimensions, those dimensions will be interpreted as batch dimensions.	required
momentum	Optional[BatchableScalar]	Momentum coefficient, expected as a scalar. If provided as a scalar, Polyak-style momentum will be enabled. If given as a tensor with multiple dimensions, those dimensions will be interpreted as batch dimensions.	None

Source code in evotorch/algorithms/functional/funcsgd.py

def sgd(
    *,
    center_init: BatchableVector,
    center_learning_rate: BatchableScalar,
    momentum: Optional[BatchableScalar] = None,
) -> SGDState:
    """
    Initialize the gradient ascent/descent search and get its initial state.

    Reference regarding the momentum behavior:

        Polyak, B. T. (1964).
        Some methods of speeding up the convergence of iteration methods.
        USSR Computational Mathematics and Mathematical Physics, 4(5):1–17.

    Args:
        center_init: Starting point for the gradient ascent/descent.
            Expected as a PyTorch tensor with at least 1 dimension.
            If there are 2 or more dimensions, the extra leftmost dimensions
            are interpreted as batch dimensions.
        center_learning_rate: Learning rate (i.e. the step size) for gradient
            ascent/descent. Can be a scalar or a multidimensional tensor.
            If given as a tensor with multiple dimensions, those dimensions
            will be interpreted as batch dimensions.
        momentum: Momentum coefficient, expected as a scalar.
            If provided as a scalar, Polyak-style momentum will be enabled.
            If given as a tensor with multiple dimensions, those dimensions
            will be interpreted as batch dimensions.
    """
    center_init = torch.as_tensor(center_init)
    dtype = center_init.dtype
    device = center_init.device

    def as_tensor(x) -> torch.Tensor:
        return torch.as_tensor(x, dtype=dtype, device=device)

    velocity = torch.zeros_like(center_init)
    center_learning_rate = as_tensor(center_learning_rate)
    momentum = as_tensor(0.0) if momentum is None else as_tensor(momentum)

    return SGDState(
        center=center_init,
        velocity=velocity,
        center_learning_rate=center_learning_rate,
        momentum=momentum,
    )

sgd_ask(state)

Get the search point stored by the given SGDState.

Parameters:

Name	Type	Description	Default
state	SGDState	The current state of gradient ascent/descent.	required

Source code in evotorch/algorithms/functional/funcsgd.py

def sgd_ask(state: SGDState) -> torch.Tensor:
    """
    Get the search point stored by the given `SGDState`.

    Args:
        state: The current state of gradient ascent/descent.
    Returns:
        The search point as a 1-dimensional tensor in the non-batched case,
        or as a multi-dimensional tensor if the search is batched.
    """
    return state.center

sgd_tell(state, *, follow_grad)

Tell the gradient ascent/descent the current gradient to get its next state.

Parameters:

Name	Type	Description	Default
state	SGDState	The current state of gradient ascent/descent.	required
follow_grad	BatchableVector	Gradient at the current point of the search. Can be a 1-dimensional tensor in the non-batched case, or a multi-dimensional tensor in the batched case.	required

Source code in evotorch/algorithms/functional/funcsgd.py

def sgd_tell(state: SGDState, *, follow_grad: BatchableVector) -> SGDState:
    """
    Tell the gradient ascent/descent the current gradient to get its next state.

    Args:
        state: The current state of gradient ascent/descent.
        follow_grad: Gradient at the current point of the search.
            Can be a 1-dimensional tensor in the non-batched case,
            or a multi-dimensional tensor in the batched case.
    Returns:
        The updated state of gradient ascent/descent, with the given gradient
        applied.
    """
    velocity, center = _sgd_step(
        follow_grad,
        state.center,
        state.velocity,
        state.center_learning_rate,
        state.momentum,
    )

    return SGDState(
        center=center,
        velocity=velocity,
        center_learning_rate=state.center_learning_rate,
        momentum=state.momentum,
    )