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Surrogate optimizers on equal call budgets

branin (d=2, 48 calls)

MethodSeedsMedian regret at half budgetMedian regretGeometric mean regretWorstMedian proposal s/run
egobox-q1100.01246.57e-085.64e-087.94e-070.78
egobox-q4100.02392.15e-074.73e-070.0002550.76
fcmaes-q4100.02683.75e-075.8e-074.83e-060.03
fcmaes-q1100.002211.51e-061.1e-068.49e-060.04
fcmaes-pass1-q4100.02761.01e-058.42e-060.0001160.03
fcmaes-pass1-q1100.03841.9e-051.52e-050.0001230.04
botorch-noiseless-q1100.02085.99e-056.87e-050.0009933.44
optuna-gp-q1100.03457.69e-058.44e-050.0002766.13
botorch-q1100.040.0002730.0002170.0025132.91
skopt-q1100.01110.0005140.0004520.0096514.39
botorch-q4100.2070.004910.003290.04138.42
biteopt100.7390.1320.1370.581–
optuna-tpe-q1100.3680.1470.1330.3830.08
cmaes100.8760.3170.2230.9–
random101.960.9380.5462.19–

hartmann3 (d=3, 48 calls)

MethodSeedsMedian regret at half budgetMedian regretGeometric mean regretWorstMedian proposal s/run
fcmaes-q1100.0005651.48e-078.09e-082.43e-070.07
fcmaes-q4100.007171.64e-071.54e-077.5e-070.03
fcmaes-pass1-q1100.0003091.16e-061.15e-065.19e-060.05
fcmaes-pass1-q4100.009252.88e-062.24e-067.41e-060.03
optuna-gp-q1100.0002622.8e-052.38e-050.0001555.28
egobox-q1100.003314.19e-054.38e-050.000230.91
egobox-q4100.008196.08e-057.84e-050.0009261.11
skopt-q1100.002520.0001460.0002430.008213.31
botorch-q1100.009850.004720.002320.0095970.96
botorch-noiseless-q1100.008020.007880.001210.0082167.57
botorch-q4100.03220.009210.006960.011939.38
optuna-tpe-q1100.3710.090.08110.3620.07
biteopt100.4250.1010.1140.608–
cmaes100.270.1280.1110.485–
random100.6380.4530.3930.885–

hartmann6 (d=6, 96 calls)

MethodSeedsMedian regret at half budgetMedian regretGeometric mean regretWorstMedian proposal s/run
fcmaes-q1100.0006594.99e-074.3e-060.1190.33
fcmaes-q4100.04339.09e-077.51e-060.1190.20
fcmaes-pass1-q1100.001655.88e-050.0001870.1190.35
fcmaes-pass1-q4100.06047.71e-050.0002890.1190.19
skopt-q1100.02720.0004660.0007710.11947.84
optuna-gp-q1100.02590.001220.004622.0713.52
botorch-noiseless-q1100.08440.002880.006950.18590.08
botorch-q1100.08840.02030.02720.188114.79
egobox-q1100.06850.05980.003230.126.31
egobox-q4100.1390.1190.008180.12611.07
optuna-tpe-q1100.4770.1570.1590.3480.25
botorch-q4100.2240.1930.1330.23172.98
cmaes101.020.4150.3470.965–
biteopt101.290.6540.560.999–
random101.31.11.091.9–

styblinski10 (d=10, 128 calls)

MethodSeedsMedian regret at half budgetMedian regretGeometric mean regretWorstMedian proposal s/run
biteopt1011016.74.9581.8–
fcmaes-q11092.256.751.385.10.89
fcmaes-q41013076.766.51110.68
optuna-tpe-q11011980.6761060.50
egobox-q11014381.968.215288.33
fcmaes-pass1-q410122848198.70.62
botorch-q11012287.878.3132200.06
skopt-q1101229290.1165129.53
fcmaes-pass1-q1101161011021621.06
optuna-gp-q11012311711214639.19
egobox-q410183129112182104.78
cmaes10166134129155–
botorch-q410163145141182252.16
random10179153149184–

rosenbrock8 (d=8, 128 calls)

MethodSeedsMedian regret at half budgetMedian regretGeometric mean regretWorstMedian proposal s/run
biteopt1076.925.37–
cmaes107777–
fcmaes-pass1-q11077770.72
fcmaes-pass1-q41077770.52
fcmaes-q110776.9970.71
fcmaes-q41077770.54
random107777–
egobox-q11085.721.924.383.345.96
skopt-q1107624.22036.2102.66
egobox-q41010927.131.611927.38
optuna-tpe-q11012632.434.41220.43

oscillator (d=2, 32 calls)

MethodSeedsMedian regret at half budgetMedian regretGeometric mean regretWorstMedian proposal s/run
fcmaes-q1100.0003979.69e-097.36e-097.7e-080.02
fcmaes-pass1-q1100.0004043.93e-082.1e-083.87e-070.02
egobox-q4100.002373.03e-073.72e-074.24e-050.24
fcmaes-q4100.000985.61e-074.54e-070.0001430.01
egobox-q1100.0003496.64e-074.77e-076.11e-050.26
optuna-gp-q1100.0002523.35e-062.08e-067.57e-063.13
fcmaes-pass1-q4100.001614.77e-062.14e-066.62e-050.01
botorch-noiseless-q1100.0001215.07e-063.91e-062.51e-0519.53
skopt-q1100.003471.57e-059.33e-066.6e-055.22
botorch-q1100.002512.45e-053.09e-050.00047611.12
botorch-q4100.002580.0002159.64e-050.0013414.69
optuna-tpe-q1100.004330.00140.0006810.003980.05
cmaes100.007060.001810.002340.0378–
biteopt100.007840.001830.001660.0134–
random100.008620.002660.002840.0251–