Ei

neps.optimizers.bayesian_optimization.acquisition_functions.ei

ComprehensiveExpectedImprovement

ComprehensiveExpectedImprovement(
    augmented_ei: bool = False,
    xi: float = 0.0,
    in_fill: str = "best",
    log_ei: bool = False,
    optimize_on_max_fidelity: bool = True,
)

Bases: BaseAcquisition

1. The input x2 is a networkx graph instead of a vectorial input

2. The search space (a collection of x1_graphs) is discrete, so there is no gradient-based optimisation. Instead, we compute the EI at all candidate points and empirically select the best position during optimisation

PARAMETER	DESCRIPTION
augmented_ei	Using the Augmented EI heuristic modification to the standard expected improvement algorithm according to Huang (2006). TYPE: bool DEFAULT: False
xi	manual exploration-exploitation trade-off parameter. TYPE: float DEFAULT: 0.0
in_fill	the criterion to be used for in-fill for the determination of mu_star 'best' means the empirical best observation so far (but could be susceptible to noise), 'posterior' means the best posterior GP mean encountered so far, and is recommended for optimization of more noisy functions. Defaults to "best". TYPE: str DEFAULT: 'best'
log_ei	log-EI if true otherwise usual EI. TYPE: bool DEFAULT: False

Source code in neps/optimizers/bayesian_optimization/acquisition_functions/ei.py

def __init__(
    self,
    augmented_ei: bool = False,
    xi: float = 0.0,
    in_fill: str = "best",
    log_ei: bool = False,
    optimize_on_max_fidelity: bool = True,
):
    """This is the graph BO version of the expected improvement
    key differences are:

    1. The input x2 is a networkx graph instead of a vectorial input

    2. The search space (a collection of x1_graphs) is discrete, so there is no
       gradient-based optimisation. Instead, we compute the EI at all candidate points
       and empirically select the best position during optimisation

    Args:
        augmented_ei: Using the Augmented EI heuristic modification to the standard
            expected improvement algorithm according to Huang (2006).
        xi: manual exploration-exploitation trade-off parameter.
        in_fill: the criterion to be used for in-fill for the determination of mu_star
            'best' means the empirical best observation so far (but could be
            susceptible to noise), 'posterior' means the best *posterior GP mean*
            encountered so far, and is recommended for optimization of more noisy
            functions. Defaults to "best".
        log_ei: log-EI if true otherwise usual EI.
    """
    super().__init__()

    if in_fill not in ["best", "posterior"]:
        raise ValueError(f"Invalid value for in_fill ({in_fill})")
    self.augmented_ei = augmented_ei
    self.xi = xi
    self.in_fill = in_fill
    self.log_ei = log_ei
    self.incumbent = None
    self.optimize_on_max_fidelity = optimize_on_max_fidelity

eval

eval(
    x: Iterable, asscalar: bool = False
) -> Union[ndarray, Tensor, float]

Return the negative expected improvement at the query point x2

Source code in neps/optimizers/bayesian_optimization/acquisition_functions/ei.py

def eval(
    self, x: Iterable, asscalar: bool = False
) -> Union[np.ndarray, torch.Tensor, float]:
    """
    Return the negative expected improvement at the query point x2
    """
    assert self.incumbent is not None, "EI function not fitted on model"
    if x[0].has_fidelity and self.optimize_on_max_fidelity:
        _x = deepcopy(x)

        [elem.set_to_max_fidelity() for elem in _x]
    else:
        _x = x
    try:
        mu, cov = self.surrogate_model.predict(_x)
    except ValueError as e:
        raise e
        # return -1.0  # in case of error. return ei of -1
    std = torch.sqrt(torch.diag(cov))
    mu_star = self.incumbent
    gauss = Normal(torch.zeros(1, device=mu.device), torch.ones(1, device=mu.device))
    # u = (mu - mu_star - self.xi) / std
    # ei = std * updf + (mu - mu_star - self.xi) * ucdf
    if self.log_ei:
        # we expect that f_min is in log-space
        f_min = mu_star - self.xi
        v = (f_min - mu) / std
        ei = torch.exp(f_min) * gauss.cdf(v) - torch.exp(
            0.5 * torch.diag(cov) + mu
        ) * gauss.cdf(v - std)
    else:
        u = (mu_star - mu - self.xi) / std
        ucdf = gauss.cdf(u)
        updf = torch.exp(gauss.log_prob(u))
        ei = std * updf + (mu_star - mu - self.xi) * ucdf
    if self.augmented_ei:
        sigma_n = self.surrogate_model.likelihood
        ei *= 1.0 - torch.sqrt(torch.tensor(sigma_n, device=mu.device)) / torch.sqrt(
            sigma_n + torch.diag(cov)
        )
    if isinstance(_x, list) and asscalar:
        return ei.detach().numpy()
    if asscalar:
        ei = ei.detach().numpy().item()
    return ei