# Source code for botorch.test_functions.multi_fidelity

#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# 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] ** 2
+ 5 / math.pi * X[..., 0]
- 6
)
t2 = 10 * (1 - 1 / (8 * math.pi)) * torch.cos(X[..., 0])
return t1**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)]

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],
]
self.register_buffer("A", torch.tensor(A, dtype=torch.float))
self.register_buffer("P", torch.tensor(P, dtype=torch.float))

[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) ** 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**2 + 0.1 * (1 - X[..., -2:-1])) ** 2
t2 = (X_curr - 1 + 0.1 * (1 - X[..., -1:]) ** 2) ** 2
return -((t1 + t2).sum(dim=-1))