Rescorla and Wagners Theory

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Rescorla and Wagners Theory
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Aristotle informed us that learning is based on
two things 1.) Contiguity Two stimuli must be
paired together 2.) Repetition The two stimuli
must be paired more than once However, Kamin
ran an experiment, where contiguity and
repetition were held constant. Despite this,
different amounts of learning took place.
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Group 1 Group 2 Tone ? Shock ----------
Light/Tone ? Shock (had less surprise) Light/Tone
? Shock (had more surprise) Light Alone ? No
fear Light Alone ? Fear No Learning about
Light Learning about light These results
cannot be explained by simple contiguity and
repetition. Kamin suggested that the two
groups differed in the amount of surprise they
experienced. He theorized that when an animal is
surprised learning will take place. Rescorla
and Wagner attempted to explain this phenomenon
in a mathematical formula. We will return to
this experiment later.
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Here learning is considered knowing something
about the associative strength between two
stimuli (the conditioned stimulus and the
unconditioned stimulus). V The
associative strength between these two stimuli
can be denoted as V. Associative strength how
strongly one stimulus is associated with another
stimulus. The variable of interest is ?V (change
in associative strength, which can increase or
decrease) on a given learning trial. ?V indicates
how much the animal learns on any given trial.
How is ?V determined on a given learning
trial?
Food
Tone
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Linguistically.and mathematically ?V is based
on (a function of) how much the animal already
knows. Specifically, it is an inverse
function. The more knowledge the animal has, the
smaller ?V (or the less the associative strength
of the two stimuli can strengthen). The less the
animal knows, the larger the ?V will be. Stated
differently. ?V ? VT Where ? asymptote of
learning and VT the current associative strength
of the tone with the US. i.e. ?V (The most
the animal can learn what the animal already
knows)
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Asymptote of learning. The highest amount of
learning possible.
R E S P O N D I N G
?V is larger near the beginning of learning. That
is, increases in associative strength are of a
greater value near the beginning of curve (when
the animal has much to learn), and become smaller
near the end of the curve (when the animal
already knows a lot).
Animal knows too much already. He cant show any
large increases in learning, because hell
surpass the asymptote. Not possible.
Where the most learning takes place.
Animal has learned nothing yet, and so the
possibility to learn a lot exists.
Trials
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?V ? - VT
But theres a problem with this. On the first
trial, VT 0, because the animal shows zero
association between the tone and the food. When
this value is plugged in to the formula ?V ?
0 ? This would mean that the animal went
from knowing nothing to knowing everything there
is to know in only one trial. Then on the second
trial, VT ? because the associative strength of
the tone with food is now as strong as it
possibly can be. When this value is plugged into
the formula ?V ? - ? 0 This would mean
that the animal learns nothing from the second
trial nor any trial thereafter. But learning
clearly depends on repetition, as Aristotle
informed us. This formula eliminates
repetition.so it must be altered.
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So Rescorla and Wagner introduced a learning rate
parameter ?V C(? VT) First, we have to set
some limits on C If C were 0, then no learning
could ever take place If C were 1, all learning
would take place on the first trial Then C is
bounded by 0 C 1 The larger C is, the
faster you learn. What determines C? C is a
function of the CS (Tone) and US (Food). The more
salient (important/noticeable) the US and CS are,
the larger C will be.
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Rescorla and Wagner introduced symbols for the CS
and US. C aß
Where a salience of CS and ß salience
of US We want to know the ?V per trial, because
we wish to quantify how much learning takes place
in one instance. ?VTrial aTßF (?
VTrial) The (aTßF) term indicates the salience
of the events (learning rate parameter). VT is
the expectation of food following the tone
(associative strength). This expectation is zero
on the first trial. So again this part of the
equation states (what actually occurs what was
expected).
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• So what Rescorla and Wagner contributed to the
  theory with this formula was that learning on a
  given trial depends on all stimuli present, not
  just on the CS.
• ?V C(?- ?V)
• where ?V The GRAND TOTAL of all the stimuli
  present with a US on given trial.
• This insight could explain the results of the
  above experiment. And it does.
• We are now in a position, to understand how
  previous conditioning to one stimulus will affect
  conditioning to a second stimulus, when presented
  together.

?VA aAß1(1-VAX) ?VX aXß1(1-VAX) Where A
the tone And X the light
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Group 1 Group 2 Tone ? Shock ----------
Light/Tone ? Shock (No associative
strength) Light/Tone ? Shock (associative
strength) Light Alone ? No fear (Had less
surprise) Light Alone ? Fear (had more
surprise) No Learning Learning In this
experiment, Group 1 was not surprised by the
outcome (shock) when the light and tone were
presented. They already learned to expect the
shock from the tone alone, so the light was
superfluous and redundant in signaling shock.
Therefore, there no associative strength was
formed between the Light and the Tone. This is
partly due to the fact that by the time the light
and the tone were presented together the
associative strength between the tone and the US
had already approached ? and (? ?) 0 No
learning Group 2, however, was surprised. They
did not expect to be shocked. Here, the light and
tone have equal significance in signaling the
shock, since there was no previous conditioning
with either of the cues. Since the expectation of
shock was zero (?- 0) ? (modified by C, of
course) learning
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?VA aAß1(1-VAX) ?VX aXß1(1-VAX) Attentional
Theory Stresses the importance of attending to a
stimulus in order to learn about it. However, the
belief is that attention may be selective rather
than divided. In this explanation, if A is
reinforced previously, and then an AX compound is
presented, the animal selectively attends to A to
the detriment of X. In general, if reinforcement
is random enough, the animal may fail to attend
to the CS. But attentional theory fails to
explain all the nuances of the data. Therefore,
Rescorla and Wagner remain skeptical.