Source code for botorch.optim.initializers

#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.

r"""
References

.. [Regis]
    R. G. Regis, C. A. Shoemaker. Combining radial basis function
    surrogates and dynamic coordinate search in high-dimensional
    expensive black-box optimization, Engineering Optimization, 2013.
"""
from __future__ import annotations

import warnings
from math import ceil
from typing import Dict, List, Optional, Tuple, Union

import torch
from botorch import settings
from botorch.acquisition.acquisition import AcquisitionFunction
from botorch.acquisition.knowledge_gradient import (
    _get_value_function,
    qKnowledgeGradient,
)
from botorch.acquisition.utils import is_nonnegative
from botorch.exceptions.errors import BotorchTensorDimensionError
from botorch.exceptions.warnings import (
    BadInitialCandidatesWarning,
    BotorchWarning,
    SamplingWarning,
)
from botorch.models.model import Model
from botorch.optim.utils import fix_features, get_X_baseline
from botorch.utils.multi_objective.pareto import is_non_dominated
from botorch.utils.sampling import (
    batched_multinomial,
    draw_sobol_samples,
    get_polytope_samples,
    manual_seed,
)
from botorch.utils.transforms import normalize, standardize, unnormalize
from torch import Tensor
from torch.distributions import Normal
from torch.quasirandom import SobolEngine


[docs]def gen_batch_initial_conditions( acq_function: AcquisitionFunction, bounds: Tensor, q: int, num_restarts: int, raw_samples: int, fixed_features: Optional[Dict[int, float]] = None, options: Optional[Dict[str, Union[bool, float, int]]] = None, inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None, equality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None, ) -> Tensor: r"""Generate a batch of initial conditions for random-restart optimziation. TODO: Support t-batches of initial conditions. Args: acq_function: The acquisition function to be optimized. bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`. q: The number of candidates to consider. num_restarts: The number of starting points for multistart acquisition function optimization. raw_samples: The number of raw samples to consider in the initialization heuristic. Note: if `sample_around_best` is True (the default is False), then `2 * raw_samples` samples are used. fixed_features: A map `{feature_index: value}` for features that should be fixed to a particular value during generation. options: Options for initial condition generation. For valid options see `initialize_q_batch` and `initialize_q_batch_nonneg`. If `options` contains a `nonnegative=True` entry, then `acq_function` is assumed to be non-negative (useful when using custom acquisition functions). In addition, an "init_batch_limit" option can be passed to specify the batch limit for the initialization. This is useful for avoiding memory limits when computing the batch posterior over raw samples. inequality constraints: A list of tuples (indices, coefficients, rhs), with each tuple encoding an inequality constraint of the form `\sum_i (X[indices[i]] * coefficients[i]) >= rhs`. equality constraints: A list of tuples (indices, coefficients, rhs), with each tuple encoding an inequality constraint of the form `\sum_i (X[indices[i]] * coefficients[i]) = rhs`. Returns: A `num_restarts x q x d` tensor of initial conditions. Example: >>> qEI = qExpectedImprovement(model, best_f=0.2) >>> bounds = torch.tensor([[0.], [1.]]) >>> Xinit = gen_batch_initial_conditions( >>> qEI, bounds, q=3, num_restarts=25, raw_samples=500 >>> ) """ options = options or {} seed: Optional[int] = options.get("seed") batch_limit: Optional[int] = options.get( "init_batch_limit", options.get("batch_limit") ) batch_initial_arms: Tensor factor, max_factor = 1, 5 init_kwargs = {} device = bounds.device bounds_cpu = bounds.cpu() if "eta" in options: init_kwargs["eta"] = options.get("eta") if options.get("nonnegative") or is_nonnegative(acq_function): init_func = initialize_q_batch_nonneg if "alpha" in options: init_kwargs["alpha"] = options.get("alpha") else: init_func = initialize_q_batch q = 1 if q is None else q # the dimension the samples are drawn from effective_dim = bounds.shape[-1] * q if effective_dim > SobolEngine.MAXDIM and settings.debug.on(): warnings.warn( f"Sample dimension q*d={effective_dim} exceeding Sobol max dimension " f"({SobolEngine.MAXDIM}). Using iid samples instead.", SamplingWarning, ) while factor < max_factor: with warnings.catch_warnings(record=True) as ws: n = raw_samples * factor if inequality_constraints is None and equality_constraints is None: if effective_dim <= SobolEngine.MAXDIM: X_rnd = draw_sobol_samples(bounds=bounds_cpu, n=n, q=q, seed=seed) else: with manual_seed(seed): # load on cpu X_rnd_nlzd = torch.rand( n, q, bounds_cpu.shape[-1], dtype=bounds.dtype ) X_rnd = bounds_cpu[0] + (bounds_cpu[1] - bounds_cpu[0]) * X_rnd_nlzd else: X_rnd = ( get_polytope_samples( n=n * q, bounds=bounds, inequality_constraints=inequality_constraints, equality_constraints=equality_constraints, seed=seed, n_burnin=options.get("n_burnin", 10000), thinning=options.get("thinning", 32), ) .view(n, q, -1) .cpu() ) # sample points around best if options.get("sample_around_best", False): X_best_rnd = sample_points_around_best( acq_function=acq_function, n_discrete_points=n * q, sigma=options.get("sample_around_best_sigma", 1e-3), bounds=bounds, subset_sigma=options.get("sample_around_best_subset_sigma", 1e-1), prob_perturb=options.get("sample_around_best_prob_perturb"), ) if X_best_rnd is not None: X_rnd = torch.cat( [ X_rnd, X_best_rnd.view(n, q, bounds.shape[-1]).cpu(), ], dim=0, ) X_rnd = fix_features(X_rnd, fixed_features=fixed_features) with torch.no_grad(): if batch_limit is None: batch_limit = X_rnd.shape[0] Y_rnd_list = [] start_idx = 0 while start_idx < X_rnd.shape[0]: end_idx = min(start_idx + batch_limit, X_rnd.shape[0]) Y_rnd_curr = acq_function( X_rnd[start_idx:end_idx].to(device=device) ).cpu() Y_rnd_list.append(Y_rnd_curr) start_idx += batch_limit Y_rnd = torch.cat(Y_rnd_list) batch_initial_conditions = init_func( X=X_rnd, Y=Y_rnd, n=num_restarts, **init_kwargs ).to(device=device) if not any(issubclass(w.category, BadInitialCandidatesWarning) for w in ws): return batch_initial_conditions if factor < max_factor: factor += 1 if seed is not None: seed += 1 # make sure to sample different X_rnd warnings.warn( "Unable to find non-zero acquisition function values - initial conditions " "are being selected randomly.", BadInitialCandidatesWarning, ) return batch_initial_conditions
[docs]def gen_one_shot_kg_initial_conditions( acq_function: qKnowledgeGradient, bounds: Tensor, q: int, num_restarts: int, raw_samples: int, fixed_features: Optional[Dict[int, float]] = None, options: Optional[Dict[str, Union[bool, float, int]]] = None, inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None, equality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None, ) -> Optional[Tensor]: r"""Generate a batch of smart initializations for qKnowledgeGradient. This function generates initial conditions for optimizing one-shot KG using the maximizer of the posterior objective. Intutively, the maximizer of the fantasized posterior will often be close to a maximizer of the current posterior. This function uses that fact to generate the initital conditions for the fantasy points. Specifically, a fraction of `1 - frac_random` (see options) is generated by sampling from the set of maximizers of the posterior objective (obtained via random restart optimization) according to a softmax transformation of their respective values. This means that this initialization strategy internally solves an acquisition function maximization problem. The remaining `frac_random` fantasy points as well as all `q` candidate points are chosen according to the standard initialization strategy in `gen_batch_initial_conditions`. Args: acq_function: The qKnowledgeGradient instance to be optimized. bounds: A `2 x d` tensor of lower and upper bounds for each column of task features. q: The number of candidates to consider. num_restarts: The number of starting points for multistart acquisition function optimization. raw_samples: The number of raw samples to consider in the initialization heuristic. fixed_features: A map `{feature_index: value}` for features that should be fixed to a particular value during generation. options: Options for initial condition generation. These contain all settings for the standard heuristic initialization from `gen_batch_initial_conditions`. In addition, they contain `frac_random` (the fraction of fully random fantasy points), `num_inner_restarts` and `raw_inner_samples` (the number of random restarts and raw samples for solving the posterior objective maximization problem, respectively) and `eta` (temperature parameter for sampling heuristic from posterior objective maximizers). inequality constraints: A list of tuples (indices, coefficients, rhs), with each tuple encoding an inequality constraint of the form `\sum_i (X[indices[i]] * coefficients[i]) >= rhs`. equality constraints: A list of tuples (indices, coefficients, rhs), with each tuple encoding an inequality constraint of the form `\sum_i (X[indices[i]] * coefficients[i]) = rhs`. Returns: A `num_restarts x q' x d` tensor that can be used as initial conditions for `optimize_acqf()`. Here `q' = q + num_fantasies` is the total number of points (candidate points plus fantasy points). Example: >>> qKG = qKnowledgeGradient(model, num_fantasies=64) >>> bounds = torch.tensor([[0., 0.], [1., 1.]]) >>> Xinit = gen_one_shot_kg_initial_conditions( >>> qKG, bounds, q=3, num_restarts=10, raw_samples=512, >>> options={"frac_random": 0.25}, >>> ) """ options = options or {} frac_random: float = options.get("frac_random", 0.1) if not 0 < frac_random < 1: raise ValueError( f"frac_random must take on values in (0,1). Value: {frac_random}" ) q_aug = acq_function.get_augmented_q_batch_size(q=q) # TODO: Avoid unnecessary computation by not generating all candidates ics = gen_batch_initial_conditions( acq_function=acq_function, bounds=bounds, q=q_aug, num_restarts=num_restarts, raw_samples=raw_samples, fixed_features=fixed_features, options=options, inequality_constraints=inequality_constraints, equality_constraints=equality_constraints, ) # compute maximizer of the value function value_function = _get_value_function( model=acq_function.model, objective=acq_function.objective, posterior_transform=acq_function.posterior_transform, sampler=acq_function.inner_sampler, project=getattr(acq_function, "project", None), ) from botorch.optim.optimize import optimize_acqf fantasy_cands, fantasy_vals = optimize_acqf( acq_function=value_function, bounds=bounds, q=1, num_restarts=options.get("num_inner_restarts", 20), raw_samples=options.get("raw_inner_samples", 1024), fixed_features=fixed_features, return_best_only=False, inequality_constraints=inequality_constraints, equality_constraints=equality_constraints, ) # sampling from the optimizers n_value = int((1 - frac_random) * (q_aug - q)) # number of non-random ICs eta = options.get("eta", 2.0) weights = torch.exp(eta * standardize(fantasy_vals)) idx = torch.multinomial(weights, num_restarts * n_value, replacement=True) # set the respective initial conditions to the sampled optimizers ics[..., -n_value:, :] = fantasy_cands[idx, 0].view(num_restarts, n_value, -1) return ics
[docs]def gen_value_function_initial_conditions( acq_function: AcquisitionFunction, bounds: Tensor, num_restarts: int, raw_samples: int, current_model: Model, fixed_features: Optional[Dict[int, float]] = None, options: Optional[Dict[str, Union[bool, float, int]]] = None, ) -> Tensor: r"""Generate a batch of smart initializations for optimizing the value function of qKnowledgeGradient. This function generates initial conditions for optimizing the inner problem of KG, i.e. its value function, using the maximizer of the posterior objective. Intutively, the maximizer of the fantasized posterior will often be close to a maximizer of the current posterior. This function uses that fact to generate the initital conditions for the fantasy points. Specifically, a fraction of `1 - frac_random` (see options) of raw samples is generated by sampling from the set of maximizers of the posterior objective (obtained via random restart optimization) according to a softmax transformation of their respective values. This means that this initialization strategy internally solves an acquisition function maximization problem. The remaining raw samples are generated using `draw_sobol_samples`. All raw samples are then evaluated, and the initial conditions are selected according to the standard initialization strategy in 'initialize_q_batch' individually for each inner problem. Args: acq_function: The value function instance to be optimized. bounds: A `2 x d` tensor of lower and upper bounds for each column of task features. num_restarts: The number of starting points for multistart acquisition function optimization. raw_samples: The number of raw samples to consider in the initialization heuristic. current_model: The model of the KG acquisition function that was used to generate the fantasy model of the value function. fixed_features: A map `{feature_index: value}` for features that should be fixed to a particular value during generation. options: Options for initial condition generation. These contain all settings for the standard heuristic initialization from `gen_batch_initial_conditions`. In addition, they contain `frac_random` (the fraction of fully random fantasy points), `num_inner_restarts` and `raw_inner_samples` (the number of random restarts and raw samples for solving the posterior objective maximization problem, respectively) and `eta` (temperature parameter for sampling heuristic from posterior objective maximizers). Returns: A `num_restarts x batch_shape x q x d` tensor that can be used as initial conditions for `optimize_acqf()`. Here `batch_shape` is the batch shape of value function model. Example: >>> fant_X = torch.rand(5, 1, 2) >>> fantasy_model = model.fantasize(fant_X, SobolQMCNormalSampler(16)) >>> value_function = PosteriorMean(fantasy_model) >>> bounds = torch.tensor([[0., 0.], [1., 1.]]) >>> Xinit = gen_value_function_initial_conditions( >>> value_function, bounds, num_restarts=10, raw_samples=512, >>> options={"frac_random": 0.25}, >>> ) """ options = options or {} seed: Optional[int] = options.get("seed") frac_random: float = options.get("frac_random", 0.6) if not 0 < frac_random < 1: raise ValueError( f"frac_random must take on values in (0,1). Value: {frac_random}" ) # compute maximizer of the current value function value_function = _get_value_function( model=current_model, objective=getattr(acq_function, "objective", None), posterior_transform=acq_function.posterior_transform, sampler=getattr(acq_function, "sampler", None), project=getattr(acq_function, "project", None), ) from botorch.optim.optimize import optimize_acqf fantasy_cands, fantasy_vals = optimize_acqf( acq_function=value_function, bounds=bounds, q=1, num_restarts=options.get("num_inner_restarts", 20), raw_samples=options.get("raw_inner_samples", 1024), fixed_features=fixed_features, return_best_only=False, options={ k: v for k, v in options.items() if k not in ("frac_random", "num_inner_restarts", "raw_inner_samples", "eta") }, ) batch_shape = acq_function.model.batch_shape # sampling from the optimizers n_value = int((1 - frac_random) * raw_samples) # number of non-random ICs if n_value > 0: eta = options.get("eta", 2.0) weights = torch.exp(eta * standardize(fantasy_vals)) idx = batched_multinomial( weights=weights.expand(*batch_shape, -1), num_samples=n_value, replacement=True, ).permute(-1, *range(len(batch_shape))) resampled = fantasy_cands[idx] else: resampled = torch.empty( 0, *batch_shape, 1, bounds.shape[-1], dtype=fantasy_cands.dtype, device=fantasy_cands.device, ) # add qMC samples randomized = draw_sobol_samples( bounds=bounds, n=raw_samples - n_value, q=1, batch_shape=batch_shape, seed=seed ).to(resampled) # full set of raw samples X_rnd = torch.cat([resampled, randomized], dim=0) X_rnd = fix_features(X_rnd, fixed_features=fixed_features) # evaluate the raw samples with torch.no_grad(): Y_rnd = acq_function(X_rnd) # select the restart points using the heuristic return initialize_q_batch( X=X_rnd, Y=Y_rnd, n=num_restarts, eta=options.get("eta", 2.0) )
[docs]def initialize_q_batch(X: Tensor, Y: Tensor, n: int, eta: float = 1.0) -> Tensor: r"""Heuristic for selecting initial conditions for candidate generation. This heuristic selects points from `X` (without replacement) with probability proportional to `exp(eta * Z)`, where `Z = (Y - mean(Y)) / std(Y)` and `eta` is a temperature parameter. When using an acquisiton function that is non-negative and possibly zero over large areas of the feature space (e.g. qEI), you should use `initialize_q_batch_nonneg` instead. Args: X: A `b x batch_shape x q x d` tensor of `b` - `batch_shape` samples of `q`-batches from a d`-dim feature space. Typically, these are generated using qMC sampling. Y: A tensor of `b x batch_shape` outcomes associated with the samples. Typically, this is the value of the batch acquisition function to be maximized. n: The number of initial condition to be generated. Must be less than `b`. eta: Temperature parameter for weighting samples. Returns: A `n x batch_shape x q x d` tensor of `n` - `batch_shape` `q`-batch initial conditions, where each batch of `n x q x d` samples is selected independently. Example: >>> # To get `n=10` starting points of q-batch size `q=3` >>> # for model with `d=6`: >>> qUCB = qUpperConfidenceBound(model, beta=0.1) >>> Xrnd = torch.rand(500, 3, 6) >>> Xinit = initialize_q_batch(Xrnd, qUCB(Xrnd), 10) """ n_samples = X.shape[0] batch_shape = X.shape[1:-2] or torch.Size() if n > n_samples: raise RuntimeError( f"n ({n}) cannot be larger than the number of " f"provided samples ({n_samples})" ) elif n == n_samples: return X Ystd = Y.std(dim=0) if torch.any(Ystd == 0): warnings.warn( "All acquisition values for raw samples points are the same for " "at least one batch. Choosing initial conditions at random.", BadInitialCandidatesWarning, ) return X[torch.randperm(n=n_samples, device=X.device)][:n] max_val, max_idx = torch.max(Y, dim=0) Z = (Y - Y.mean(dim=0)) / Ystd etaZ = eta * Z weights = torch.exp(etaZ) while torch.isinf(weights).any(): etaZ *= 0.5 weights = torch.exp(etaZ) if batch_shape == torch.Size(): idcs = torch.multinomial(weights, n) else: idcs = batched_multinomial( weights=weights.permute(*range(1, len(batch_shape) + 1), 0), num_samples=n ).permute(-1, *range(len(batch_shape))) # make sure we get the maximum if max_idx not in idcs: idcs[-1] = max_idx if batch_shape == torch.Size(): return X[idcs] else: return X.gather( dim=0, index=idcs.view(*idcs.shape, 1, 1).expand(n, *X.shape[1:]) )
[docs]def initialize_q_batch_nonneg( X: Tensor, Y: Tensor, n: int, eta: float = 1.0, alpha: float = 1e-4 ) -> Tensor: r"""Heuristic for selecting initial conditions for non-neg. acquisition functions. This function is similar to `initialize_q_batch`, but designed specifically for acquisition functions that are non-negative and possibly zero over large areas of the feature space (e.g. qEI). All samples for which `Y < alpha * max(Y)` will be ignored (assuming that `Y` contains at least one positive value). Args: X: A `b x q x d` tensor of `b` samples of `q`-batches from a `d`-dim. feature space. Typically, these are generated using qMC. Y: A tensor of `b` outcomes associated with the samples. Typically, this is the value of the batch acquisition function to be maximized. n: The number of initial condition to be generated. Must be less than `b`. eta: Temperature parameter for weighting samples. alpha: The threshold (as a fraction of the maximum observed value) under which to ignore samples. All input samples for which `Y < alpha * max(Y)` will be ignored. Returns: A `n x q x d` tensor of `n` `q`-batch initial conditions. Example: >>> # To get `n=10` starting points of q-batch size `q=3` >>> # for model with `d=6`: >>> qEI = qExpectedImprovement(model, best_f=0.2) >>> Xrnd = torch.rand(500, 3, 6) >>> Xinit = initialize_q_batch(Xrnd, qEI(Xrnd), 10) """ n_samples = X.shape[0] if n > n_samples: raise RuntimeError("n cannot be larger than the number of provided samples") elif n == n_samples: return X max_val, max_idx = torch.max(Y, dim=0) if torch.any(max_val <= 0): warnings.warn( "All acquisition values for raw sampled points are nonpositive, so " "initial conditions are being selected randomly.", BadInitialCandidatesWarning, ) return X[torch.randperm(n=n_samples, device=X.device)][:n] # make sure there are at least `n` points with positive acquisition values pos = Y > 0 num_pos = pos.sum().item() if num_pos < n: # select all positive points and then fill remaining quota with randomly # selected points remaining_indices = (~pos).nonzero(as_tuple=False).view(-1) rand_indices = torch.randperm(remaining_indices.shape[0], device=Y.device) sampled_remaining_indices = remaining_indices[rand_indices[: n - num_pos]] pos[sampled_remaining_indices] = 1 return X[pos] # select points within alpha of max_val, iteratively decreasing alpha by a # factor of 10 as necessary alpha_pos = Y >= alpha * max_val while alpha_pos.sum() < n: alpha = 0.1 * alpha alpha_pos = Y >= alpha * max_val alpha_pos_idcs = torch.arange(len(Y), device=Y.device)[alpha_pos] weights = torch.exp(eta * (Y[alpha_pos] / max_val - 1)) idcs = alpha_pos_idcs[torch.multinomial(weights, n)] if max_idx not in idcs: idcs[-1] = max_idx return X[idcs]
[docs]def sample_points_around_best( acq_function: AcquisitionFunction, n_discrete_points: int, sigma: float, bounds: Tensor, best_pct: float = 5.0, subset_sigma: float = 1e-1, prob_perturb: Optional[float] = None, ) -> Optional[Tensor]: r"""Find best points and sample nearby points. Args: acq_function: The acquisition function. n_discrete_points: The number of points to sample. sigma: The standard deviation of the additive gaussian noise for perturbing the best points. bounds: A `2 x d`-dim tensor containing the bounds. best_pct: The percentage of best points to perturb. subset_sigma: The standard deviation of the additive gaussian noise for perturbing a subset of dimensions of the best points. prob_perturb: The probability of perturbing each dimension. Returns: An optional `n_discrete_points x d`-dim tensor containing the sampled points. This is None if no baseline points are found. """ X = get_X_baseline(acq_function=acq_function) if X is None: return with torch.no_grad(): try: posterior = acq_function.model.posterior(X) except AttributeError: warnings.warn( "Failed to sample around previous best points.", BotorchWarning, ) return mean = posterior.mean while mean.ndim > 2: # take average over batch dims mean = mean.mean(dim=0) try: f_pred = acq_function.objective(mean) # Some acquisition functions do not have an objective # and for some acquisition functions the objective is None except (AttributeError, TypeError): f_pred = mean if hasattr(acq_function, "maximize"): # make sure that the optimiztaion direction is set properly if not acq_function.maximize: f_pred = -f_pred try: # handle constraints for EHVI-based acquisition functions constraints = acq_function.constraints if constraints is not None: neg_violation = -torch.stack( [c(mean).clamp_min(0.0) for c in constraints], dim=-1 ).sum(dim=-1) feas = neg_violation == 0 if feas.any(): f_pred[~feas] = float("-inf") else: # set objective equal to negative violation f_pred = neg_violation except AttributeError: pass if f_pred.ndim == mean.ndim and f_pred.shape[-1] > 1: # multi-objective # find pareto set is_pareto = is_non_dominated(f_pred) best_X = X[is_pareto] else: if f_pred.shape[-1] == 1: f_pred = f_pred.squeeze(-1) n_best = max(1, round(X.shape[0] * best_pct / 100)) # the view() is to ensure that best_idcs is not a scalar tensor best_idcs = torch.topk(f_pred, n_best).indices.view(-1) best_X = X[best_idcs] n_trunc_normal_points = ( n_discrete_points // 2 if best_X.shape[-1] >= 20 else n_discrete_points ) perturbed_X = sample_truncated_normal_perturbations( X=best_X, n_discrete_points=n_trunc_normal_points, sigma=sigma, bounds=bounds, ) if best_X.shape[-1] > 20 or prob_perturb is not None: perturbed_subset_dims_X = sample_perturbed_subset_dims( X=best_X, bounds=bounds, # ensure that we return n_discrete_points n_discrete_points=n_discrete_points - n_trunc_normal_points, sigma=sigma, prob_perturb=prob_perturb, ) perturbed_X = torch.cat([perturbed_X, perturbed_subset_dims_X], dim=0) # shuffle points perm = torch.randperm(perturbed_X.shape[0], device=X.device) perturbed_X = perturbed_X[perm] return perturbed_X
[docs]def sample_truncated_normal_perturbations( X: Tensor, n_discrete_points: int, sigma: float, bounds: Tensor, qmc: bool = True, ) -> Tensor: r"""Sample points around `X`. Sample perturbed points around `X` such that the added perturbations are sampled from N(0, sigma^2 I) and truncated to be within [0,1]^d. Args: X: A `n x d`-dim tensor starting points. n_discrete_points: The number of points to sample. sigma: The standard deviation of the additive gaussian noise for perturbing the points. bounds: A `2 x d`-dim tensor containing the bounds. qmc: A boolean indicating whether to use qmc. Returns: A `n_discrete_points x d`-dim tensor containing the sampled points. """ X = normalize(X, bounds=bounds) d = X.shape[1] # sample points from N(X_center, sigma^2 I), truncated to be within # [0, 1]^d. if X.shape[0] > 1: rand_indices = torch.randint(X.shape[0], (n_discrete_points,), device=X.device) X = X[rand_indices] if qmc: std_bounds = torch.zeros(2, d, dtype=X.dtype, device=X.device) std_bounds[1] = 1 u = draw_sobol_samples(bounds=std_bounds, n=n_discrete_points, q=1).squeeze(1) else: u = torch.rand((n_discrete_points, d), dtype=X.dtype, device=X.device) # compute bounds to sample from a = -X b = 1 - X # compute z-score of bounds alpha = a / sigma beta = b / sigma normal = Normal(0, 1) cdf_alpha = normal.cdf(alpha) # use inverse transform perturbation = normal.icdf(cdf_alpha + u * (normal.cdf(beta) - cdf_alpha)) * sigma # add perturbation and clip points that are still outside perturbed_X = (X + perturbation).clamp(0.0, 1.0) return unnormalize(perturbed_X, bounds=bounds)
[docs]def sample_perturbed_subset_dims( X: Tensor, bounds: Tensor, n_discrete_points: int, sigma: float = 1e-1, qmc: bool = True, prob_perturb: Optional[float] = None, ) -> Tensor: r"""Sample around `X` by perturbing a subset of the dimensions. By default, dimensions are perturbed with probability equal to `min(20 / d, 1)`. As shown in [Regis]_, perturbing a small number of dimensions can be beneificial. The perturbations are sampled from N(0, sigma^2 I) and truncated to be within [0,1]^d. Args: X: A `n x d`-dim tensor starting points. `X` must be normalized to be within `[0, 1]^d`. bounds: The bounds to sample perturbed values from n_discrete_points: The number of points to sample. sigma: The standard deviation of the additive gaussian noise for perturbing the points. qmc: A boolean indicating whether to use qmc. prob_perturb: The probability of perturbing each dimension. If omitted, defaults to `min(20 / d, 1)`. Returns: A `n_discrete_points x d`-dim tensor containing the sampled points. """ if bounds.ndim != 2: raise BotorchTensorDimensionError("bounds must be a `2 x d`-dim tensor.") elif X.ndim != 2: raise BotorchTensorDimensionError("X must be a `n x d`-dim tensor.") d = bounds.shape[-1] if prob_perturb is None: # Only perturb a subset of the features prob_perturb = min(20.0 / d, 1.0) if X.shape[0] == 1: X_cand = X.repeat(n_discrete_points, 1) else: rand_indices = torch.randint(X.shape[0], (n_discrete_points,), device=X.device) X_cand = X[rand_indices] pert = sample_truncated_normal_perturbations( X=X_cand, n_discrete_points=n_discrete_points, sigma=sigma, bounds=bounds, qmc=qmc, ) # find cases where we are not perturbing any dimensions mask = ( torch.rand( n_discrete_points, d, dtype=bounds.dtype, device=bounds.device, ) <= prob_perturb ) ind = (~mask).all(dim=-1).nonzero() # perturb `n_perturb` of the dimensions n_perturb = ceil(d * prob_perturb) perturb_mask = torch.zeros(d, dtype=mask.dtype, device=mask.device) perturb_mask[:n_perturb].fill_(1) # TODO: use batched `torch.randperm` when available: # https://github.com/pytorch/pytorch/issues/42502 for idx in ind: mask[idx] = perturb_mask[torch.randperm(d, device=bounds.device)] # Create candidate points X_cand[mask] = pert[mask] return X_cand