Testfunctions function

Test functions of x

Several test functions of varying complexity are available. They are defined on [0,1].

guirland(x)

sin1(x)

difficult(x)

difficult2(x)

double_sine(x, rho1 = 0.3, rho2 = 0.8, tmax = 0.5)

Arguments

• x: vector specifying the location where the function is to be evaluated.
• rho1, rho2, tmax: additional parameters for double_sine.

Details

These test functions are translated from the Matlab and Python codes in the references.

Examples

par(mfrow = c(2,3))

curve(guirland, n = 501)
curve(sin1)
curve(difficult, xlim = c(1e-8, 1), n = 1001)
xgrid <- seq(0, 1, length.out = 500)
plot(xgrid, sapply(xgrid, difficult2), type = 'l', ylab = "difficult2(x)")
plot(xgrid, sapply(xgrid, double_sine), type = 'l', ylab = "double_sine(x) (default)")
double_sine2 <- function(x) double_sine(x, rho1 = 0.8, rho2 = 0.3)
plot(xgrid, sapply(xgrid, double_sine2), type = 'l', ylab = "double_sine(x) (modified)")

par(mfrow = c(1,1))

References

M. Valko, A. Carpentier and R. Munos (2013), Stochastic Simultaneous Optimistic Optimization, ICML, 19-27 https://inria.hal.science/hal-00789606. Matlab code: https://team.inria.fr/sequel/software/StoSOO/.

J.-B. Grill, M. Valko and R. Munos (2015), Black-box optimization of noisy functions with unknown smoothness, NIPS, 667-675 https://inria.hal.science/hal-01222915. Python code: https://team.inria.fr/sequel/software/POO/.