Design of Experiments - Design of Experiments for Reinforcement Learning - page 54

Fig. 3.2 An ideal design of
experiments has overlapping
regions among the desired
information, analytic method,
and the experiment
characteristics. In real
experiments, there may be no
overlapping region and a
trade-off must be made in one
or more of these areas.

Experiment/
response
characteristics

Desired
information

Analytic
method

The classical and contemporary techniques take slightly different approaches to de-
signing and analyzing experiments because the systems or processes under study
often have unique and different characteristics. This section describes these two dif-
ferent types of experiments and some methods related to their design and analysis.
We do not provide an exhaustive review, and the interested reader is directed to
more comprehensive works for a more thorough review of these methods, especially
Montgomery ( 2008 ) and the references in this section.

3.1 Classical Design of Experiments

In this work, we define classical design of experiments to be those techniques that
were developed largely for discovering knowledge about physical and real-world
processes or systems. Some of these methods include (fractional) factorial designs,
analysis of variance (ANOVA), Taguchi methods, and response surface modeling.
Though many of these methods were developed decades ago, and in spite of their rela-
tive simplicity, they have proven to be extremely useful. The types of experiments we
consider are those that primarily relate to determining the effects of factors or interac-
tions between factors. The types of experiments or situations for which these methods
are most suitable include those with random experimental error, relatively few fac-
tors, and relatively few factor-levels. Additionally, classical design of experiments
approaches require practices of randomization, replication, and blocking.
Experimental error is the random and uncontrollable variation of a response vari-
able (Montgomery 2008 ). More specifically, for the same factor-level combination,
the response will have some natural variation and it will have a non-deterministic
response. Due to this experimental error, a common practice is to spread out design
points to obtain more accurate factor effect estimates. These experimental techniques