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from __future__ import annotations
import math
import numpy as np
def get_warm_start_mgd(
source_solutions: list[tuple[np.ndarray, float]],
gamma: float = 0.1,
alpha: float = 0.1,
) -> tuple[np.ndarray, float, np.ndarray]:
"""Estimates a promising distribution of the source task, then
returns a multivariate gaussian distribution (the mean vector
and the covariance matrix) used for initialization of the CMA-ES.
Args:
source_solutions:
List of solutions (parameter, value) on a source task.
gamma:
top-(gamma x 100)% solutions are selected from a set of solutions
on a source task. (default: 0.1).
alpha:
prior parameter for the initial covariance matrix (default: 0.1).
Returns:
The tuple of mean vector, sigma, and covariance matrix.
"""
# Paper: https://arxiv.org/abs/2012.06932
assert 0 < gamma <= 1, "gamma should be in (0, 1]"
if len(source_solutions) == 0:
raise ValueError("solutions should contain one or more items.")
# Select top-(gamma x 100)% solutions
source_solutions = sorted(source_solutions, key=lambda t: t[1])
gamma_n = math.floor(len(source_solutions) * gamma)
assert gamma_n >= 1, "One or more solutions must be selected from a source task"
dim = len(source_solutions[0][0])
top_gamma_solutions = np.empty(
shape=(
gamma_n,
dim,
),
dtype=float,
)
for i in range(gamma_n):
top_gamma_solutions[i] = source_solutions[i][0]
# Estimation of a Promising Distribution of a Source Task.
first_term = alpha**2 * np.eye(dim)
cov_term = np.zeros(shape=(dim, dim), dtype=float)
for i in range(gamma_n):
cov_term += np.dot(
top_gamma_solutions[i, :].reshape(dim, 1),
top_gamma_solutions[i, :].reshape(dim, 1).T,
)
second_term = cov_term / gamma_n
mean_term = np.zeros(
shape=(
dim,
1,
),
dtype=float,
)
for i in range(gamma_n):
mean_term += top_gamma_solutions[i, :].reshape(dim, 1)
mean_term /= gamma_n
third_term = np.dot(mean_term, mean_term.T)
mu = mean_term
mean = mu[:, 0]
Sigma = first_term + second_term - third_term
det_sigma = np.linalg.det(Sigma)
sigma = math.pow(det_sigma, 1.0 / 2.0 / dim)
cov = Sigma / math.pow(det_sigma, 1.0 / dim)
return mean, sigma, cov
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