DifferentiableObjective

sgptools.methods.DifferentiableObjective

Bases: Method

Informative sensor placement / path planning by directly differentiating through the objective function.

The sensing locations (or waypoints) are represented as TensorFlow variables, and a first-order optimizer (e.g., L-BFGS, Adam) is used to minimize a scalar loss built from the objective and constraints. This can be more sample-efficient than black-box methods, but is more sensitive to local minima.

Attributes

transform: Optional transform applied to the current solution. X_sol: TensorFlow variable representing the current solution locations. objective: Objective object that maps (transformed) sensing locations to a scalar value.

Source code in sgptools/methods.py

class DifferentiableObjective(Method):
    """
    Informative sensor placement / path planning by directly differentiating
    through the objective function.

    The sensing locations (or waypoints) are represented as TensorFlow
    variables, and a first-order optimizer (e.g., L-BFGS, Adam) is used to
    minimize a scalar loss built from the objective and constraints. This can
    be more sample-efficient than black-box methods, but is more sensitive to
    local minima.

    Attributes
    ----------
    transform:
        Optional transform applied to the current solution.
    X_sol:
        TensorFlow variable representing the current solution locations.
    objective:
        Objective object that maps (transformed) sensing locations to a scalar
        value.
    """

    def __init__(self,
                 num_sensing: int,
                 X_objective: np.ndarray,
                 kernel: gpflow.kernels.Kernel,
                 noise_variance: float,
                 transform: Optional[Transform] = None,
                 num_robots: int = 1,
                 X_candidates: Optional[np.ndarray] = None,
                 num_dim: Optional[int] = None,
                 objective: Union[str, Objective] = 'SLogMI',
                 X_init: Optional[np.ndarray] = None,
                 X_time: Optional[np.ndarray] = None,
                 orientation: bool = False,
                 **kwargs: Any):
        """
        Initialize a differentiable-objective method.

        Parameters
        ----------
        num_sensing:
            Number of sensing locations per robot.
        X_objective:
            Array of shape `(n, d)` used to define the objective (e.g., GP
            training inputs).
        kernel:
            GPflow kernel used inside the objective.
        noise_variance:
            Observation noise variance used inside the objective.
        transform:
            Optional transform applied to the solution before evaluating the
            objective and constraints.
        num_robots:
            Number of robots / agents. The total number of optimized points is
            `num_sensing * num_robots`.
        X_candidates:
            Optional candidate set `(c, d)` to which the final continuous
            solution can be snapped.
        num_dim:
            Dimensionality of sensing locations. If `None`, defaults to
            `X_objective.shape[-1]`, or to `X_init.shape[-1]` if given.
        objective:
            Objective specification (string key or `Objective` instance) used to
            construct the reward function.
        X_init:
            Initial sensing locations with shape `(num_sensing * num_robots, d)`.
            If `None`, points are selected via `get_inducing_pts`. If given,
            its dimensionality overrides `num_dim`.
        X_time:
            (Reserved for future use with spatio-temporal models; not used
            directly here.)
        orientation:
            If `True` and `X_init` is not provided, `get_inducing_pts` may add
            an orientation dimension to the initial points.
        **kwargs:
            Additional keyword arguments forwarded to the objective constructor
            when `objective` is a string.
        """
        super().__init__(num_sensing, X_objective, kernel, noise_variance,
                         transform, num_robots, X_candidates, num_dim)
        self.transform = transform
        if X_candidates is None:
            self.X_candidates = X_objective  # Default candidates to objective points

        if X_init is None:
            X_init = get_inducing_pts(X_objective,
                                      num_sensing * self.num_robots,
                                      orientation=orientation)
        else:
            # Override num_dim with the dimensionality of the initial solution
            self.num_dim = X_init.shape[-1]
        self.X_sol = tf.Variable(X_init, dtype=X_init.dtype)

        if isinstance(objective, str):
            self.objective = get_objective(objective)(X_objective, kernel,
                                                      noise_variance, **kwargs)
        else:
            self.objective = objective

    def update(self, kernel: gpflow.kernels.Kernel,
               noise_variance: float) -> None:
        """
        Update the kernel and noise variance used by the objective.

        Parameters
        ----------
        kernel:
            New GPflow kernel instance.
        noise_variance:
            New observation noise variance.
        """
        self.objective.update(kernel, noise_variance)

    def get_hyperparameters(self) -> Tuple[gpflow.kernels.Kernel, float]:
        """
        Return the current kernel and noise variance used by the objective.

        Returns
        -------
        (gpflow.kernels.Kernel, float)
            A deep copy of the kernel and the current noise variance.
        """
        return deepcopy(self.objective.kernel), \
               self.objective.noise_variance

    def optimize(self,
                 max_steps: int = 500,
                 optimizer: str = 'scipy.L-BFGS-B',
                 verbose: bool = False,
                 **kwargs: Any) -> np.ndarray:
        """
        Optimize sensing locations by differentiating through the objective.

        `self.X_sol` is treated as a trainable variable and optimized using the
        specified optimizer and the internal `_objective` as the scalar loss.

        Parameters
        ----------
        max_steps:
            Maximum number of optimization steps. Defaults to 500.
        optimizer:
            Optimizer specification `"backend.method"` (e.g., `'scipy.L-BFGS-B'`,
            `'tf.adam'`) passed to `optimize_model`.
        verbose:
            If `True`, print progress information during optimization.
        **kwargs:
            Extra keyword arguments forwarded to `optimize_model`.

        Returns
        -------
        np.ndarray
            Array of shape `(num_robots, num_sensing, num_dim)` containing the
            optimized sensing locations.
        """
        _ = optimize_model(
            training_loss=self._objective,
            max_steps=max_steps,
            trainable_variables=[self.X_sol],
            optimizer=optimizer,
            verbose=verbose,
            **kwargs)

        sol: tf.Tensor = self.X_sol
        if self.transform is not None:
            sol = self.transform.expand(sol,
                                        expand_sensor_model=False)
        if not isinstance(sol, np.ndarray):
            sol_np = sol.numpy()
        else:
            sol_np = sol

        # Snap to candidate set if provided
        if self.X_candidates is not None:
            sol_np = cont2disc(sol_np, self.X_candidates)

        sol_np = sol_np.reshape(self.num_robots, -1, self.num_dim)
        return sol_np

    def _objective(self) -> float:
        """
        Scalar loss function used by `optimize_model`.

        The objective is built as:

        .. code-block:: text

            loss = objective(X_expanded) + constraint_penalty

        where both terms are produced by the `Transform`. Depending on the
        sign conventions of `objective` and `constraints`, this loss can be
        interpreted as either a negative reward or a penalized reward. The
        optimizer *minimizes* this loss.

        Returns
        -------
        tf.Tensor
            Scalar TensorFlow value representing the loss to minimize.
        """
        constraint_penality: float = 0.0
        if self.transform is not None:
            X_expanded = self.transform.expand(self.X_sol)
            constraint_penality = self.transform.constraints(self.X_sol)
            reward = self.objective(X_expanded)  # maximize (before sign handling)
        else:
            reward = self.objective(self.X_sol)  # maximize (before sign handling)

        # Transform constraints are typically <= 0; adding them penalizes violations.
        reward += constraint_penality
        return reward

__init__(num_sensing, X_objective, kernel, noise_variance, transform=None, num_robots=1, X_candidates=None, num_dim=None, objective='SLogMI', X_init=None, X_time=None, orientation=False, **kwargs)

Initialize a differentiable-objective method.

Parameters

num_sensing: Number of sensing locations per robot. X_objective: Array of shape (n, d) used to define the objective (e.g., GP training inputs). kernel: GPflow kernel used inside the objective. noise_variance: Observation noise variance used inside the objective. transform: Optional transform applied to the solution before evaluating the objective and constraints. num_robots: Number of robots / agents. The total number of optimized points is num_sensing * num_robots. X_candidates: Optional candidate set (c, d) to which the final continuous solution can be snapped. num_dim: Dimensionality of sensing locations. If None, defaults to X_objective.shape[-1], or to X_init.shape[-1] if given. objective: Objective specification (string key or Objective instance) used to construct the reward function. X_init: Initial sensing locations with shape (num_sensing * num_robots, d). If None, points are selected via get_inducing_pts. If given, its dimensionality overrides num_dim. X_time: (Reserved for future use with spatio-temporal models; not used directly here.) orientation: If True and X_init is not provided, get_inducing_pts may add an orientation dimension to the initial points. **kwargs: Additional keyword arguments forwarded to the objective constructor when objective is a string.

Source code in sgptools/methods.py

def __init__(self,
             num_sensing: int,
             X_objective: np.ndarray,
             kernel: gpflow.kernels.Kernel,
             noise_variance: float,
             transform: Optional[Transform] = None,
             num_robots: int = 1,
             X_candidates: Optional[np.ndarray] = None,
             num_dim: Optional[int] = None,
             objective: Union[str, Objective] = 'SLogMI',
             X_init: Optional[np.ndarray] = None,
             X_time: Optional[np.ndarray] = None,
             orientation: bool = False,
             **kwargs: Any):
    """
    Initialize a differentiable-objective method.

    Parameters
    ----------
    num_sensing:
        Number of sensing locations per robot.
    X_objective:
        Array of shape `(n, d)` used to define the objective (e.g., GP
        training inputs).
    kernel:
        GPflow kernel used inside the objective.
    noise_variance:
        Observation noise variance used inside the objective.
    transform:
        Optional transform applied to the solution before evaluating the
        objective and constraints.
    num_robots:
        Number of robots / agents. The total number of optimized points is
        `num_sensing * num_robots`.
    X_candidates:
        Optional candidate set `(c, d)` to which the final continuous
        solution can be snapped.
    num_dim:
        Dimensionality of sensing locations. If `None`, defaults to
        `X_objective.shape[-1]`, or to `X_init.shape[-1]` if given.
    objective:
        Objective specification (string key or `Objective` instance) used to
        construct the reward function.
    X_init:
        Initial sensing locations with shape `(num_sensing * num_robots, d)`.
        If `None`, points are selected via `get_inducing_pts`. If given,
        its dimensionality overrides `num_dim`.
    X_time:
        (Reserved for future use with spatio-temporal models; not used
        directly here.)
    orientation:
        If `True` and `X_init` is not provided, `get_inducing_pts` may add
        an orientation dimension to the initial points.
    **kwargs:
        Additional keyword arguments forwarded to the objective constructor
        when `objective` is a string.
    """
    super().__init__(num_sensing, X_objective, kernel, noise_variance,
                     transform, num_robots, X_candidates, num_dim)
    self.transform = transform
    if X_candidates is None:
        self.X_candidates = X_objective  # Default candidates to objective points

    if X_init is None:
        X_init = get_inducing_pts(X_objective,
                                  num_sensing * self.num_robots,
                                  orientation=orientation)
    else:
        # Override num_dim with the dimensionality of the initial solution
        self.num_dim = X_init.shape[-1]
    self.X_sol = tf.Variable(X_init, dtype=X_init.dtype)

    if isinstance(objective, str):
        self.objective = get_objective(objective)(X_objective, kernel,
                                                  noise_variance, **kwargs)
    else:
        self.objective = objective

get_hyperparameters()

Return the current kernel and noise variance used by the objective.

Returns

(gpflow.kernels.Kernel, float) A deep copy of the kernel and the current noise variance.

Source code in sgptools/methods.py

def get_hyperparameters(self) -> Tuple[gpflow.kernels.Kernel, float]:
    """
    Return the current kernel and noise variance used by the objective.

    Returns
    -------
    (gpflow.kernels.Kernel, float)
        A deep copy of the kernel and the current noise variance.
    """
    return deepcopy(self.objective.kernel), \
           self.objective.noise_variance

optimize(max_steps=500, optimizer='scipy.L-BFGS-B', verbose=False, **kwargs)

Optimize sensing locations by differentiating through the objective.

self.X_sol is treated as a trainable variable and optimized using the specified optimizer and the internal _objective as the scalar loss.

Parameters

max_steps: Maximum number of optimization steps. Defaults to 500. optimizer: Optimizer specification "backend.method" (e.g., 'scipy.L-BFGS-B', 'tf.adam') passed to optimize_model. verbose: If True, print progress information during optimization. **kwargs: Extra keyword arguments forwarded to optimize_model.

Returns

np.ndarray Array of shape (num_robots, num_sensing, num_dim) containing the optimized sensing locations.

Source code in sgptools/methods.py

def optimize(self,
             max_steps: int = 500,
             optimizer: str = 'scipy.L-BFGS-B',
             verbose: bool = False,
             **kwargs: Any) -> np.ndarray:
    """
    Optimize sensing locations by differentiating through the objective.

    `self.X_sol` is treated as a trainable variable and optimized using the
    specified optimizer and the internal `_objective` as the scalar loss.

    Parameters
    ----------
    max_steps:
        Maximum number of optimization steps. Defaults to 500.
    optimizer:
        Optimizer specification `"backend.method"` (e.g., `'scipy.L-BFGS-B'`,
        `'tf.adam'`) passed to `optimize_model`.
    verbose:
        If `True`, print progress information during optimization.
    **kwargs:
        Extra keyword arguments forwarded to `optimize_model`.

    Returns
    -------
    np.ndarray
        Array of shape `(num_robots, num_sensing, num_dim)` containing the
        optimized sensing locations.
    """
    _ = optimize_model(
        training_loss=self._objective,
        max_steps=max_steps,
        trainable_variables=[self.X_sol],
        optimizer=optimizer,
        verbose=verbose,
        **kwargs)

    sol: tf.Tensor = self.X_sol
    if self.transform is not None:
        sol = self.transform.expand(sol,
                                    expand_sensor_model=False)
    if not isinstance(sol, np.ndarray):
        sol_np = sol.numpy()
    else:
        sol_np = sol

    # Snap to candidate set if provided
    if self.X_candidates is not None:
        sol_np = cont2disc(sol_np, self.X_candidates)

    sol_np = sol_np.reshape(self.num_robots, -1, self.num_dim)
    return sol_np

update(kernel, noise_variance)

Update the kernel and noise variance used by the objective.

Parameters

kernel: New GPflow kernel instance. noise_variance: New observation noise variance.

Source code in sgptools/methods.py

def update(self, kernel: gpflow.kernels.Kernel,
           noise_variance: float) -> None:
    """
    Update the kernel and noise variance used by the objective.

    Parameters
    ----------
    kernel:
        New GPflow kernel instance.
    noise_variance:
        New observation noise variance.
    """
    self.objective.update(kernel, noise_variance)