Source code for botorch.test_functions.multi_fidelity

#!/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"""
Synthetic functions for multi-fidelity optimization benchmarks.
"""

from __future__ import annotations

import math
from typing import Optional

import torch
from botorch.test_functions.synthetic import SyntheticTestFunction
from torch import Tensor


[docs] class AugmentedBranin(SyntheticTestFunction): r"""Augmented Branin test function for multi-fidelity optimization. 3-dimensional function with domain `[-5, 10] x [0, 15] * [0,1]`, where the last dimension of is the fidelity parameter: B(x) = (x_2 - (b - 0.1 * (1 - x_3))x_1^2 + c x_1 - r)^2 + 10 (1-t) cos(x_1) + 10 Here `b`, `c`, `r` and `t` are constants where `b = 5.1 / (4 * math.pi ** 2)` `c = 5 / math.pi`, `r = 6`, `t = 1 / (8 * math.pi)`. B has infinitely many minimizers with `x_1 = -pi, pi, 3pi` and `B_min = 0.397887` """ dim = 3 _bounds = [(-5.0, 10.0), (0.0, 15.0), (0.0, 1.0)] _optimal_value = 0.397887 _optimizers = [ # this is a subset, ther are infinitely many optimizers (-math.pi, 12.275, 1), (math.pi, 1.3867356039019576, 0.1), (math.pi, 1.781519779945532, 0.5), (math.pi, 2.1763039559891064, 0.9), ]
[docs] def evaluate_true(self, X: Tensor) -> Tensor: t1 = ( X[..., 1] - (5.1 / (4 * math.pi**2) - 0.1 * (1 - X[..., 2])) * X[..., 0].pow(2) + 5 / math.pi * X[..., 0] - 6 ) t2 = 10 * (1 - 1 / (8 * math.pi)) * torch.cos(X[..., 0]) return t1.pow(2) + t2 + 10
[docs] class AugmentedHartmann(SyntheticTestFunction): r"""Augmented Hartmann synthetic test function. 7-dimensional function (typically evaluated on `[0, 1]^7`), where the last dimension is the fidelity parameter. H(x) = -(ALPHA_1 - 0.1 * (1-x_7)) * exp(- sum_{j=1}^6 A_1j (x_j - P_1j) ** 2) - sum_{i=2}^4 ALPHA_i exp( - sum_{j=1}^6 A_ij (x_j - P_ij) ** 2) H has a unique global minimizer `x = [0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573, 1.0]` with `H_min = -3.32237` """ dim = 7 _bounds = [(0.0, 1.0) for _ in range(7)] _optimal_value = -3.32237 _optimizers = [(0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573, 1.0)] _check_grad_at_opt = False def __init__(self, noise_std: Optional[float] = None, negate: bool = False) -> None: r""" Args: noise_std: Standard deviation of the observation noise. negate: If True, negate the function. """ super().__init__(noise_std=noise_std, negate=negate) self.register_buffer("ALPHA", torch.tensor([1.0, 1.2, 3.0, 3.2])) A = [ [10, 3, 17, 3.5, 1.7, 8], [0.05, 10, 17, 0.1, 8, 14], [3, 3.5, 1.7, 10, 17, 8], [17, 8, 0.05, 10, 0.1, 14], ] P = [ [1312, 1696, 5569, 124, 8283, 5886], [2329, 4135, 8307, 3736, 1004, 9991], [2348, 1451, 3522, 2883, 3047, 6650], [4047, 8828, 8732, 5743, 1091, 381.0], ] self.register_buffer("A", torch.tensor(A)) self.register_buffer("P", torch.tensor(P))
[docs] def evaluate_true(self, X: Tensor) -> Tensor: self.to(device=X.device, dtype=X.dtype) inner_sum = torch.sum( self.A * (X[..., :6].unsqueeze(-2) - 0.0001 * self.P).pow(2), dim=-1 ) alpha1 = self.ALPHA[0] - 0.1 * (1 - X[..., 6]) H = ( -(torch.sum(self.ALPHA[1:] * torch.exp(-inner_sum)[..., 1:], dim=-1)) - alpha1 * torch.exp(-inner_sum)[..., 0] ) return H
[docs] class AugmentedRosenbrock(SyntheticTestFunction): r"""Augmented Rosenbrock synthetic test function for multi-fidelity optimization. d-dimensional function (usually evaluated on `[-5, 10]^(d-2) * [0, 1]^2`), where the last two dimensions are the fidelity parameters: f(x) = sum_{i=1}^{d-1} (100 (x_{i+1} - x_i^2 + 0.1 * (1-x_{d-1}))^2 + (x_i - 1 + 0.1 * (1 - x_d)^2)^2) f has one minimizer for its global minimum at `z_1 = (1, 1, ..., 1)` with `f(z_i) = 0.0`. """ _optimal_value = 0.0 def __init__( self, dim=3, noise_std: Optional[float] = None, negate: bool = False ) -> None: r""" Args: dim: The (input) dimension. Must be at least 3. noise_std: Standard deviation of the observation noise. negate: If True, negate the function. """ if dim < 3: raise ValueError( "AugmentedRosenbrock must be defined it at least 3 dimensions" ) self.dim = dim self._bounds = [(-5.0, 10.0) for _ in range(self.dim)] self._optimizers = [tuple(1.0 for _ in range(self.dim))] super().__init__(noise_std=noise_std, negate=negate)
[docs] def evaluate_true(self, X: Tensor) -> Tensor: X_curr = X[..., :-3] X_next = X[..., 1:-2] t1 = 100 * (X_next - X_curr.pow(2) + 0.1 * (1 - X[..., -2:-1])).pow(2) t2 = (X_curr - 1 + 0.1 * (1 - X[..., -1:]).pow(2)).pow(2) return -((t1 + t2).sum(dim=-1))