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the created or observed object
per se
, but by the algorithmic compression
progress
(or prediction
progress
) of the subjective, learning observer.
While Kant already placed the finite, subjective human observer in the centre of
our universe (Kant
1781
), the Formal Theory of Creativity formalises some of his
ideas, viewing the subjective observer as a parameter: one cannot tell whether some-
thing is art without taking into account the individual observer's current state. This
is compatible with the musings of Danto who also wrote that one cannot objectively
tell whether something is art by simply looking at it (Danto
1981
).
To summarise, most previous ideas on the interestingness of aesthetic objects fo-
cused on their complexity, but ignored the
change
of subjective complexity through
learning. This change, however, is precisely the central ingredient of the Formal
Theory of Creativity.
12.3 Formal Details
Skip this section if you are not interested in formal details.
A learning agent's single life consists of discrete cycles or time steps
t
=
1
,
2
,...,T
. The agent's total lifetime
T
may or may not be known in advance.
At any given
t
the agent receives a real-valued environmental input vector
x(t)
and
executes a real-valued action
y(t)
which may affect future inputs. At times
t<T
its goal is to maximise future
utility
T
r(τ)
u(t)
=
E
μ
h(
≤
t)
,
(12.1)
τ
=
t
+
1
where the reward
r(t)
is a special real-valued input (vector) at time
t
,
h(t)
is
the triple
[
x(t), y(t), r(t)
]
,
h(
≤
t)
is the known history
h(
1
), h(
2
), . . . , h(t)
, and
E
μ
(
)
denotes the conditional expectation operator with respect to some typically
unknown distribution
μ
from a set
·|·
M
M
reflects
whatever is known about the possible probabilistic reactions of the environment.
For example,
of possible distributions. Here
may contain all computable distributions (Solomonoff
1978
,Li
and Vitányi
1997
, Hutter
2005
), thus essentially including all environments one
could write scientific papers about. There is just one life, so no need for predefined
repeatable trials, and the utility function implicitly takes into account the expected
remaining lifespan
E
μ
(T
M
t))
and thus the possibility to extend the lifespan
through actions (Schmidhuber
2009d
).
To maximise
u(t)
, the agent may profit from an improving, predictive
model p
of the consequences of its possible interactions with the environment. At any time
t
(1
|
h(
≤
≤
t<T
), the model
p(t)
will depend on the observed history
h(
≤
t)
. It may be
viewed as the current explanation or description of
h(
t)
, and may help to predict
and increase future rewards (Schmidhuber
1991b
). Let
C(p,h)
denote some given
model
p
's quality or performance evaluated on a history
h
. Natural performance
measures will be discussed below.
≤
