Methodology - Design of Experiments for Reinforcement Learning - page 81

Table 4.3 Convergent subregion domains after sequential CART modeling.
Domain # x 1 x 2

− −

13 [ 0.700, 0.811) [ 1.106, 1.018)

23 [ − 1.950, − 1.369) [0.513, 1.018)

28 [1.241, 1.944) [ − 0.982, − 0.534)

Domain # P conv No. Dim. ratio Min. dim. Max. dim. Ave. radius Sum radii

points

13 0.812 160 2.108 0.252 0.531 0.196 0.783

23 0.797 148 1.304 0.097 0.126 0.056 0.223

28 0.806 144 1.046 0.112 0.117 0.057 0.229

Fig. 4.4 The convergent
subregions of the 2D
camelback function following
sequential CART modeling
are enclosed in dotted lines .
These subregions nicely
surround the low regions of
the function, shown as white
in the contour plot.

23

13

28

−3 −2 −1 0 1 2 3

x 1

which is quantified by one standard deviation of the parameter bounds, are relatively
small. These numbers are clearly dependent on many parameters of the sequential
CART algorithm, including the CART model settings and the experimental designs,
though this provides an example of the potential variability of the parameter bounds.

4.2 Kriging Metamodeling

The use of metamodels to replace computationally expensive simulations is becom-
ing increasingly common. Metamodels are essentially models that approximate the
response surface of some input-output function. The purpose of metamodels is to