Page 43 - Rapid Learning in Robotics

3.3 Learning as Approximation Problem 29

Usually, the process of learning is based on a certain amount of apriori
knowledge and a set of training examples. Its goal is two-fold:

the learner should be able to recognize the re-occurance of a previ-
ously seen situation (stimuli or input) and associate the correct an-
swer (response or output) as learned before;

in new, previously un-experienced situations, the learner should gen-
eralize its knowledge and infer the answer appropriately.

The primary problem of learning is to find an appropriate representa-
tion of the learned knowledge or skill: its input (stimuli) and output (re-
sponses). The reason is rather simple and fundamental: no system can
learn, what it cannot represent.
We can distinguish three basic types of task describing variables x:

1. the orderable, continuous valued representations (e.g. length, speed,
temperature, force) with a defined order relation (x i j ) and an ex- x
isting distance metric jx i x j j;

2. a periodic or circular variable representation (e.g. azimuth angles,
hour of the day) with defined distance, but without a clear order
relation (“wrap-around”; is Monday before or after Saturday?);

3. the symbolic and categorical representation x c k g, like c f
cities, attributes and generally names. Here, nor an order, neither a
distance relation between x i and x j does exist, just the binary equiv-
alence relation is defined (x i x j ,or x i x j ).

Sometimes variables are represented depending on the context, e.g. “red”
color may get coded as category, as circular hue value, or as orderable
location in the color triangle.
A desired skill can be modeled as the mapping between an input space
in
and an output space. The input space (later notated X ) captures all
relevant system (observable and non-observed) variables. The problem of
learning such a mapping is then equivalent to the problem of synthesizing
an associative memory (Poggio and Girosi 1990). The appropriate output
is retrieved when the input is presented and the system generalizes when
a new input is presented. Different frameworks of this problem depend
strongly on the type of input and output variables.