Table 4:
Means and standard deviations of the third quartiles of $RDEμ/rsucc$ for ML-estimated and fixed hyperparameter values of the DTS-CMA-ES GP models. The third quartiles are from $2×15$ independent datasets per function and dimension, and the means and standard deviations are averaged across $2×23$ data (24 COCO functions without Linear slope$f5$ in the first and second half of optimization run) for each respective dimension.
covar. fun.$μ(x)$$ℓ$2-D3-D5-D10-D20-D
$KMate´rnν=5/2$ ML estimate ML estimate 0.41 $±0.07$ $0.39$ $±0.07$ $0.33$ $±0.06$ $0.31$ $±0.08$ $0.31$ $±0.12$
$KMate´rnν=5/2$ ML estimate $ℓ=1$ 0.41 $±0.06$ 0.39 $±0.07$ 0.38 $±0.07$ 0.42 $±0.06$ 0.45 $±0.08$
$KMate´rnν=5/2$ $mμ=0$ ML estimate 0.45 $±0.08$ 0.42 $±0.08$ 0.37 $±0.09$ 0.33 $±0.08$ 0.33 $±0.11$
$KMate´rnν=5/2$ $mμ=0$ $ℓ=1$ $0.40$ $±0.06$ 0.39 $±0.07$ 0.39 $±0.07$ 0.44 $±0.06$ 0.49 $±0.07$
$KSE$ ML estimate ML estimate 0.41 $±0.07$ 0.39 $±0.07$ 0.35 $±0.05$ 0.32 $±0.08$ 0.37 $±0.13$
$KSE$ ML estimate $ℓ=1$ 0.41 $±0.06$ 0.40 $±0.07$ 0.39 $±0.07$ 0.42 $±0.06$ 0.47 $±0.09$
$KSE$ $mμ=0$ ML estimate 0.45 $±0.09$ 0.44 $±0.09$ 0.39 $±0.08$ 0.36 $±0.10$ 0.58 $±0.34$
$KSE$ $mμ=0$ $ℓ=1$ 0.41 $±0.06$ 0.41 $±0.07$ 0.40 $±0.07$ 0.44 $±0.06$ 0.51 $±0.09$
covar. fun.$μ(x)$$ℓ$2-D3-D5-D10-D20-D
$KMate´rnν=5/2$ ML estimate ML estimate 0.41 $±0.07$ $0.39$ $±0.07$ $0.33$ $±0.06$ $0.31$ $±0.08$ $0.31$ $±0.12$
$KMate´rnν=5/2$ ML estimate $ℓ=1$ 0.41 $±0.06$ 0.39 $±0.07$ 0.38 $±0.07$ 0.42 $±0.06$ 0.45 $±0.08$
$KMate´rnν=5/2$ $mμ=0$ ML estimate 0.45 $±0.08$ 0.42 $±0.08$ 0.37 $±0.09$ 0.33 $±0.08$ 0.33 $±0.11$
$KMate´rnν=5/2$ $mμ=0$ $ℓ=1$ $0.40$ $±0.06$ 0.39 $±0.07$ 0.39 $±0.07$ 0.44 $±0.06$ 0.49 $±0.07$
$KSE$ ML estimate ML estimate 0.41 $±0.07$ 0.39 $±0.07$ 0.35 $±0.05$ 0.32 $±0.08$ 0.37 $±0.13$
$KSE$ ML estimate $ℓ=1$ 0.41 $±0.06$ 0.40 $±0.07$ 0.39 $±0.07$ 0.42 $±0.06$ 0.47 $±0.09$
$KSE$ $mμ=0$ ML estimate 0.45 $±0.09$ 0.44 $±0.09$ 0.39 $±0.08$ 0.36 $±0.10$ 0.58 $±0.34$
$KSE$ $mμ=0$ $ℓ=1$ 0.41 $±0.06$ 0.41 $±0.07$ 0.40 $±0.07$ 0.44 $±0.06$ 0.51 $±0.09$
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