On Fri, 14 Nov 2014, Stanley Nilsen via AGI wrote:
Okay, I'll see if I can grasp 2.3 and 2.4.
Perhaps you can lessen my pain by telling me which equations address a risk
factor?
Sorry to hear this is causing you pain.
Risk is in equaton (2.4):
v(ha) = \sum_{o \in O} \rho(o | ha) v(hao)
In English, this says that the value of an action
a after histor h, denoted v(ha), is von Neumann
and Morgenstern's lottery of possible outcomes
from that action. The possible outcomes are the
hao, for different observations o \in O. Each
outcome hao has value v(hao) and probability
\rho(o | ha).
Risk comes in because some outcomes may have very
low value v(hao). Those values are multiplied by
the probability of the outcome, denoted
\rho(o | ha). The sum adds up the good outcomes
(high v(hao)) and the bad outcomes (low v(hao)),
multiplied by their probabilities, so get an
expected value v(ha) of the action a.
So the sum is balancing risk (low values v(hao))
against reward (high values v(hao)). Then
equations (2.3) and (2.5) choose the action that
maximizes expected value.
Cheers,
Bill
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