Rescorla-Wagner (1972)
Theory of Classical
Conditioning
Rescorla-Wagner Theory (1972)
• Organisms only learn when events violate
their expectations (like Kamin’s surprise
hypothesis)
• Expectations are built up when ‘significant’
events follow a stimulus complex
• These expectations are only modified when
consequent events disagree with the
composite expectation
Rescorla-Wagner Theory
• These concepts were incorporated into a
mathematical formula:
– Change in the associative strength of a stimulus
depends on the existing associative strength of
that stimulus and all others present
– If existing associative strength is low, then
potential change is high; If existing associative
strength is high, then very little change occurs
– The speed and asymptotic level of learning is
determined by the strength of the CS and UCS
Rescorla-Wagner Mathematical
Formula
∆Vcs = c (Vmax – Vall)
•
•
•
•
V = associative strength
∆ = change (the amount of change)
c = learning rate parameter
Vmax = the maximum amount of associative strength
that the UCS can support
• Vall = total amount of associative strength for all
stimuli present
• Vcs = associative strength to the CS
Before conditioning begins:
• Vmax = 100 (number is arbitrary & based
on the strength of the UCS)
• Vall = 0 (because no conditioning has
occurred)
• Vcs = 0 (no conditioning has occurred yet)
• c = .5 (c must be a number between 0 and
1.0 and is a result of multiplying the CS
intensity by the UCS intensity)
First Conditioning Trial
c (Vmax - Vall)
.5 * 100 0
=
=
100
Associative Strength (V)
Trial
1
80
60
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vcs
50
Second Conditioning Trial
c (Vmax
.5 * 100
- Vall)
- 50
=
=
100
Associative Strength (V)
Trial
2
80
75
60
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vcs
25
Third Conditioning Trial
Trial
3
c (Vmax
.5 * 100
- Vall)
75
=
=
Associative Strength (V)
100
87.5
80
75
60
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vcs
12.5
4th Conditioning Trial
c (Vmax
.5 * 100
- Vall)
87.5
100
Associative Strength (V)
Trial
4
87.5
80
=
=
93.75
75
60
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vcs
6.25
5th Conditioning Trial
c
(Vmax - Vall)
.5 * 100
- 93.75
100
Associative Strength (V)
Trial
5
87.5
80
=
=
96.88
93.75
75
60
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vcs
3.125
6th Conditioning Trial
c
(Vmax - Vall)
.5 * 100
- 96.88
100
Associative Strength (V)
Trial
6
87.5
80
=
=
96.8898.44
93.75
75
60
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vcs
1.56
7th Conditioning Trial
c
(Vmax - Vall)
.5 * 100
- 98.44
100
Associative Strength (V)
Trial
7
87.5
80
=
=
96.8898.4499.22
93.75
75
60
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vcs
.78
8th Conditioning Trial
Trial
8
c
(Vmax - Vall)
.5 * 100
- 99.22
Associative Strength (V)
100
87.5
80
93.75
=
=
96.8898.44 99.22 99.61
75
60
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vcs
.39
1st Extinction Trial
Trial
1
c
(Vmax - Vall)
.5 *
0
99.61
=
=
∆Vcs
-49.8
Extinction
100
80
60
40
Vall
20
0
0
1
2
3
4
Trials
5
6
7
8
Associative Strength (V)
Associative Strength (V)
Acquisition
100
99.61
80
Vall
60
49.8
40
20
0
0
1
2
3
Trials
4
5
6
2nd Extinction Trial
Acquisition
87.5
80100
Associative Strength (V)
Associative Strength (V)
100
60
40
c
(Vmax - Vall)
.5 *
0
49.8
75
80
60
50
40
Vall
Vall
20 20
0
93.75
0
0
0
0
1
1
2
2
3
3
=
=
4 5 6 7 8
4 5 6 7 8
Trials
Trials
∆Vcs
-24.9
Extinction
96.88 98.44 99.22 99.61
Associative Strength (V)
Trial
2
100
99.61
80
Vall
60
49.8
40
24.9
20
0
0
1
2
3
Trials
4
5
6
Extinction Trials
Trial
3
c
(Vmax - Vall)
.5 *
0
12.45
=
=
∆Vcs
-12.46
Trial
4
c
(Vmax - Vall)
.5 *
0
6.23
=
=
∆Vcs
-6.23
Trial
5
c
(Vmax - Vall)
.5 *
0
3.11
=
=
∆Vcs
-3.11
Trial
6
c
(Vmax - Vall)
.5 *
0
1.56
=
=
∆Vcs
-1.56
Hypothetical Acquisition &
Extinction Curves with c=.5 and
Vmax = 100
Extinction
100
Associative Strength (V)
Associative Strength (V)
Acquisition
80
60
40
Vall
20
0
0
1
2
3
4
Trials
5
6
7
8
100
99.61
Vall
80
60
49.8
40
24.9
20
12.45
6.23
0
0
1
2
3
Trials
4
3.11
5
1.56
6
Acquisition & Extinction Curves
with c=.5 vs. c=.2 (Vmax = 100)
Extinction
120
Associative Strength (V)
Associative Strength (V)
Acquisition
100
80
60
40
20
0
0
1
2
3
4
Trials
5
6
7
8
120
100
80
c=.5
60
c=.2
40
c=.5
c=.2
20
0
0
1
2
3
Trials
4
5
6
Theory Handles other Phenomena
• Overshadowing
– Whenever there are multiple stimuli or a compound
stimulus, then Vall = Vcs1 + Vcs2
• Trial 1:
– ∆Vnoise = .2 (100 – 0) = (.2)(100) = 20
– ∆Vlight = .3 (100 – 0) = (.3)(100) = 30
– Total Vall = current Vall + ∆Vnoise + ∆Vlight = 0 +20 +30 =50
• Trial 2:
– ∆Vnoise = .2 (100 – 50) = (.2)(50) = 10
– ∆Vlight = .3 (100 – 50) = (.3)(50) = 15
– Total Vall = current Vall + ∆Vnoise + ∆Vlight = 50+10+15=75
Theory Handles other Phenomena
• Blocking
– Clearly, the first 16 trials in Phase 1 will result in most
of the Vmax accruing to the first CS, leaving very little
Vmax available to the second CS in Phase 2
• Overexpectation Effect
– When CSs trained separately (where both are close to
Vmax) are then presented together you’ll actually get a
decrease in associative strength
Rescorla-Wagner Model
• The theory is not perfect:
– Can’t handle configural learning without a little
tweaking
– Can’t handle latent inhibition
• But, it has been the “best” theory of
Classical Conditioning