The Rescorla-Wagner model provides a mathematical framework for Pavlovian conditioning. It states that the change in associative strength (ΔVn) on each trial is proportional to the difference between the maximum possible strength (λ) and the current strength (Vn-1). This results in a negatively accelerated learning curve as the difference gets smaller with more training. During extinction, when the unconditioned stimulus is no longer presented, associative strength decreases on each trial as it becomes less and less surprising. The model can account for many classical and operant conditioning phenomena through simple associative learning rules.

1.  Instructor: David A. Townsend
 Email:
 Class Web Page:

2. RESCORLA-WAGNER THEORY:
BACKGROUND
 Research by Rescorla and Kamin requires a
change in our conception of conditioning.
 Animals do not evaluate CS-US pairings in
isolation.
 Evaluation occurs against a background that
includes: unpaired presentations of CS and US,
or presentations of other CSs, or general
experimental context.
 Conditioning is most likely to occur when
evaluation of entire situation reveals that a CS is
best available predictor of US.

3. RESCORLA-WAGNER THEORY:
BACKGROUND
 This view of Pavlovian conditioning makes
conditioning process appear much more
complex than it had seemed.
 How do animals do it?
 By what means do animals keep track of CSs
and USs, estimate probabilities, compute
probability differences, and make CRs to CS?
 If such calculations do occur, then animals are
likely to make them automatically.
 We need an account of the mechanism by which
such automatic calculation might occur.

4. RESCORLA-WAGNER THEORY:
BACKGROUND
 In last 30 years, many different theories have
been advanced to explain rich details of
Pavlovian conditioning.
 Most influential account was that of Robert A.
Rescorla and Allan R. Wagner in 1972.
 All later theories have been responses to
shortcomings of Rescorla-Wagner account.
 So, we will focus on Rescorla-Wagner theory.

5. RESCORLA-WAGNER THEORY:
PRELUDE
 Kamin’s blocking effect set stage for RescorlaWagner model.
 Blocking effect suggested to Kamin that USs
were only effective when they were
SURPRISING or unpredicted by CSs.
 However, USs were not effective when they
were unsurprising or predicted by CSs.
 Added CS was not associated with any change
in US.

6. RESCORLA-WAGNER THEORY:
OVERVIEW
 Rescorla-Wagner theory explains complex
contingency analysis in terms of simple
associations of the sort Pavlov envisioned.
 It can account for most standard conditioning
phenomena in Chapter 3 as well as many newer
phenomena in Chapter 4.
 Theory is also precise; specified in such clear
detail that one can derive predictions about
behavior in untested experimental situations.
Mathematically

7. RESCORLA-WAGNER THEORY:
TUTORIALS
If you need help, then please consult:
http://psy.uq.oz.au/~landcp/PY269/rwmodel/index.html
http://www.biols.susx.ac.uk/home/Martin_
Yeomans/Learning/Lecture6.html
http://www.psych.ualberta.ca/~msnyder/Ac
ademic/Psych_281/C5/Ch5page.html

8. RESCORLA-WAGNER THEORY:
ACQUISITION
 Standard conditioning curves are negatively
accelerated.
 Changes in conditioning strength are very
substantial early in training.
 But, as training proceeds, a leveling-off point, or
asymptote, is approached.
 Generally speaking, changes in strength of
conditioning get smaller with each trial.

9. RESCORLA-WAGNER THEORY:
ACQUISITION
 Negatively accelerated learning curve suggests
that organism does not profit equally from each
training trial.
 How much one profits depends on how much
one already knows:
When one knows nothing, profits are substantial (US
surprise is high).
When one knows a great deal, profits from further trials
are small (US surprise is low).

10. RESCORLA-WAGNER THEORY:
ACQUISITION
 Rather than learning a fixed amount with each
trial, one learns a fixed proportion of difference
between one’s present level of learning and
maximum possible.
 As difference gets smaller (as one learns more),
amount of new learning produced by further
trials gets smaller.
 Rescorla-Wagner model simply builds in a
mathematical expression that conforms to
negatively accelerated learning function.

11. RESCORLA-WAGNER THEORY:
ACQUISITION
 Here is the equation:
∆Vn = K( — Vn-1)
 V, associative strength, is measure of learning.
 It is a theoretical quantity.
 It is not equivalent to magnitude or probability of
any particular CR.
 But, it is assumed to be closely related to such
measures of conditioned responding.

12. RESCORLA-WAGNER THEORY:
ACQUISITION
 ∆Vn = K( — Vn-1)
 K reflects salience of CS.
 K can vary between 0 and 1 (0 ≤ K ≤ 1).
 Bigger K, bigger change in V on any given trial.
 Thus, salient stimuli mean large Ks, which mean
large ∆Vs, which mean large changes in
association from trial to trial.
Intensity
Sensory modality
Organism
Types of US’s employed ( belongingness)

13. RESCORLA-WAGNER THEORY:
ACQUISITION
 ∆Vn = K( — Vn-1)
 indicates that different USs support different
maximum levels of conditioning.
 Asymptote of conditioning will vary with US;
different asymptotes are reflected by different
s.
 More intense US, higher asymptote of
conditioning, and higher .
 is always equal to or greater than 0 ( ≥ 0).

14. RESCORLA-WAGNER THEORY:
ACQUISITION
 ∆Vn = K( — Vn-1)
 Change in strength on Trial n (∆Vn) is
proportional to difference between and prior
associative strength Vn-1.
 Because V grows from trial to trial, quantity ( Vn-1) gets smaller and smaller, so ∆Vn also gets
smaller and smaller, generating a negatively
accelerated learning curve.
 Eventually, V will equal , so that ( - Vn-1) will
be 0, and conditioning will be complete
(asymptote will be reached).

15. ∆Vn = K( — Vn-1)
∆ (change in) Delta
 V, associative strength, is measure of learning
 K reflects salience of CS.
 ( Lambda) indicates that different USs support
different maximum levels of conditioning.
Change in strength on Trial n (∆Vn) is
proportional to difference between and
Vn-1 prior associative strength.

16. Acquisition Trials
First conditioning trial:
Light (CS) is paired with shock (US)
∆Vn= light (CS)=0
k = .20
= associated
strength of shock
= 100
∆Vn = K( — Vn-1)
∆ (change in) Delta
V, associative strength,
is measure of learning
K reflects salience of CS
and US.
( Lambda) indicates that
different USs support
different maximum levels
of conditioning.
Change in strength on
Trial n (∆Vn) is
proportional to difference
between and
Vn-1 prior associative
strength.
First Trial
∆Vn=k( -Vn-1)
∆Vn= .20(100-0)
∆Vn = .20 units

17. ∆Vn = K( — Vn-1)
Acquisition Trials
First conditioning trial:
Light (CS) is paired with shock (US)
∆Vtotal= light (CS)=0
k = .20
= associated
strength of shock
= 100
∆ (change in) Delta
V, associative strength, is
measure of learning
K reflects salience of CS and
US.
( Lambda) indicates that
different USs support different
maximum levels of
conditioning.
Change in strength on Trial n
(∆Vn) is proportional to
difference between and
Vn-1 prior associative strength.
Second Trial
∆Vn=k( -Vn-1)
∆Vn= .20(100-20)
∆Vn = .16 units

18. ∆Vn = K( — Vn-1)
Acquisition Trials
First conditioning trial:
Light (CS) is paired with shock (US)
∆Vtotal= light (CS)=0
k = .20
= associated
strength of shock
= 100
∆ (change in) Delta
V, associative strength, is
measure of learning
K reflects salience of CS and
US.
( Lambda) indicates that
different USs support different
maximum levels of
conditioning.
Change in strength on Trial n
(∆Vn) is proportional to
difference between and
Vn-1 prior associative strength.
Third Trial
∆Vn=k( -Vn-1)
∆Vn= .20(100-36)
∆Vn = .12.8 units

19. ∆Vn = K( — Vn-1)
Acquisition Trials
First conditioning trial:
Light (CS) is paired with shock (US)
∆Vtotal= light (CS)=0
k = .20
= associated
strength of shock
= 100
∆ (change in) Delta
V, associative strength, is
measure of learning
K reflects salience of CS and
US.
( Lambda) indicates that
different USs support different
maximum levels of
conditioning.
Change in strength on Trial n
(∆Vn) is proportional to
difference between and
Vn-1 prior associative strength.
Forth Trial
∆Vn=k( -Vn-1)
∆Vn= .20(100-48.8)
∆Vn = .10.2 units
N= trial4, N-1= trial 3

20. Rescorla-Wagner Model
 Calculations from
the RescorlaWagner model
show a
mathematical
relationship to the
process of
conditioning
60
50
40
30
Vtotal
20
10
0
trial
0
trial
2
trail
4

21. 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
 Surprise

22. First Conditioning Trial
Trial
1
K ( - Vn-1 )
.5 * 100 -
=
0
∆Vn
=
50
Associative Strength (V)
100
80
∆Vn = K( — Vn-1)
60
50
40
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆ (change in) Delta
V, associative strength, is
measure of learning
K reflects salience of CS and
US.
( Lambda) indicates that
different USs support different
maximum levels of
conditioning.
Change in strength on Trial n
(∆Vn) is proportional to
difference between and
Vn-1 prior associative strength.

23. Second Conditioning Trial
K ( - Vn-1 )
.5 * 100 -50
∆Vn
25
=
=
100
Associative Strength (V)
Trial
2
80
75
60
50
40
20
0
0
0
1
2
3
4
Trials
5
6
7
8

24. Third Conditioning Trial
K ( - Vn-1 )
.5 * 100 -75
∆Vn
12.5
=
=
100
Associative Strength (V)
Trial
3
87.5
80
75
60
50
40
20
0
0
0
1
2
3
4
Trials
5
6
7
8

25. 4th Conditioning Trial
K ( - Vn-1 )
c (Vmax .5 * 100
-
87.5
80
∆Vn
∆Vcs
6.25
=
=
=
Vall)
87.5
100
Associative Strength (V)
Trial
Trial
4
93.75
75
60
∆Vcs = c (Vmax – Vall)
50
40
Vall
20
0
0
0
1
2
3
4
Trials
5
6
7
8

26. 5th Conditioning Trial
K ( - Vn-1 )
.5 * 10 - 93.75
100
Associative Strength (V)
Trial
5
87.5
80
=
=
96.88
93.75
75
60
50
40
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vn
3.125

27. 6th Conditioning Trial
K ( - Vn-1 )
.5 * 100 - 96.88
100
Associative Strength (V)
Trial
6
87.5
80
=
=
96.8898.44
93.75
75
60
50
40
20
0
0
0
1
2
3
4
Trials
5
6
7
8
∆Vn
1.56

28. 7th Conditioning Trial
Trial
7
K ( - Vn-1 )
.5 * 100 - 98.44
Associative Strength (V)
100
87.5
80
=
=
96.8898.4499.22
93.75
∆Vn = K( — Vn-1)
75
60
50
40
20
0
0
0
1
2
∆Vn
.78
3
4
Trials
5
6
7
8
∆ (change in) Delta
V, associative strength, is
measure of learning
K reflects salience of CS and
US.
( Lambda) indicates that
different USs support different
maximum levels of
conditioning.
Change in strength on Trial n
(∆Vn) is proportional to
difference between and
Vn-1 prior associative strength.

29. 8th Conditioning Trial
K ( - Vn-1 )
.5 * 1 - 99.22
100
Associative Strength (V)
Trial
8
87.5
80
∆Vn
.39
=
=
93.75
96.8898.44 99.22 99.61
75
60
50
40
20
0
0
0
1
2
3
4
Trials
5
6
7
8

30. 1st Extinction Trial
Trial
1
K ( - Vn-1 )
.5 * 0 -99.61
∆Vn
-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
60
49.8
40
20
0
0
1
2
3
Trials
4
5
6

31. 2nd Extinction Trial
K ( - Vn-1 )
.5 *
0 -49.8
Acquisition
60
40
93.75
87.5
80 100
Associative Strength (V)
Associative Strength (V)
100
75
80
60
50
40
Vall
20 20
0
0
0
0
0
1
1
2
2
3
3
4
4
Trials
Trials
5
5
6
6
7
7
8
8
∆Vn
-24.9
=
=
Extinction
96.88 98.44 99.22 99.61
Associative Strength (V)
Trial
2
100
99.61
80
60
49.8
40
24.9
20
0
0
1
2
3
Trials
4
5
6

32. Extinction Trials
Trial
3
K ( Vn-1 )
.5 *
0
12.45
Less and Less surprising
=
=
∆Vn
-12.46
4
.5 *
0
-
6.23
=
-6.23
5
.5 *
0
-
3.11
=
-3.11
6
.5 *
0
-
1.56
=
-1.56

33. Hypothetical Acquisition & Extinction
Curves with K=.5 and = 100
100
Extinction
Associative Strength (V)
Associative Strength (V)
Acquisition
80
60
40
20
100
99.61
80
60
49.8
40
24.9
20
12.45
0
0
0
1
2
3
4
Trials
5
6
7
8
6.23
0
1
2
3
Trials
4
3.11
5
1.56
6

34. Acquisition & Extinction Curves with
c=.5 vs. c=.2 ( = 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

35. RESCORLA-WAGNER THEORY:
COMPETITION
 Key feature of Rescorla-Wagner model is how it
explains conditioning with compound stimuli
comprising two or more elements.
 Associative strength of a compound stimulus is
assumed to equal the sum of associative
strengths of elements.
 VAX = VA + VX
 Here, A and X may have different saliences, K
and M, respectively.

36. ∆Vn = K( — Vn-1)
 ∆ (change in) Delta
 V, associative strength, is measure of learning
 K reflects salience of CS.

( Lambda) indicates that different USs support different maximum levels
of conditioning.
 Change in strength on Trial n (∆Vn) is proportional to difference
between and
 Vn-1 prior associative strength.
A,X symbols used for multiple CS’s
Salience with multiple CS’s: A=K,
X=M

37. RESCORLA-WAGNER THEORY:
OVERSHADOWING
 VAX = VA + VX
 How can theory account for overshadowing?
 With equally salient stimuli, VX would attain only
.50 rather than 1.00 if X alone were trained-mutual overshadowing.
 Increases in salience of A would further reduce
VX from .50 toward .00.
 If salience of A (K) is very high and salience of X
(M) is very low, then overshadowing should be
complete.

38. Eyeblink Conditioning: OVERSHADOWING
Training: Tone/light + Shock
Tone = Eyeblink  CR
Light = ?
No CR to light
Corneal Air Puff
Elicits Eyeblink Response
Corneal Air Puff
Given with Tone
Tone Given Alone
Elicits Eyeblink Response

39. Overshadowing:
 Overshadowing
 Whenever there are multiple stimuli
or a compound stimulus,
then ∆Vn = Vcs1 (K) + Vcs2 (M)
∆Vn = K( — Vn-1)
 Trial 1:
∆Vnoise = .2 (100 – 0) = (.2)(100) = 20
∆Vlight = .3 (100 – 0) = (.3)(100) = 30
Total ∆Vn = ∆ (K)Vnoise + ∆Vlight = 0 +20 +30 =50
 Trial 2:
Noise= 30
∆Vnoise = .2 (100 – 50) = (.2)(50) = 10
∆Vlight = .3 (100 – 50) = (.3)(50) = 15
Light= 45
Total ∆Vn = Vn-1 + ∆Vnoise + ∆Vlight = 50+10+15=75

40. Overshadowing
Trial 1: VA = .40(100 – 0) = 40
Vx = .10(100 – 0) = 10
Trial 2: VA = .40(100 – 50) = 20
Vx = .10(100 – 50) = 5
T2:
A=60
X=15

41. RESCORLA-WAGNER THEORY:
BLOCKING
 VAX = VA + VX
 How would theory account for blocking?
 With equally salient stimuli, VX would be only .50
rather than 1.00 if AX only were trained.
 Prior training with A would further reduce VX,
because VA would already be substantial before
AX trials were introduced.
 Extensive training with A should lead to
complete blocking of X.

42. Blocking
Group
Phase 1
Experimental
A
Group (blocking)
Control
Group
US
Nothing
Phase 2
Phase 3
AB
US
Test B
AB
US
Test B
Same # trials
Contiguity
Contingency

43. RESCORLA-WAGNER THEORY:
BLOCKING
A
Associative Strength (V)
Acquisition
100
80
60
40
X
20
0
0
1
2
3
4
Trials
5
6
7
8
?

44. The Rescorla-Wagner associative model of conditioning is based upon
four assumptions that refer to the process by which the CS and UC gain
associative strength
 (1) a particular US can only support a specific
level of conditioning,
 (2) associative strength increases with each
reinforced trial, but depends upon prior
conditioning,
 (3) particular CSs and US can support different
rates of conditioning and
 (4) when two or more stimuli are paired with the
UC, the stimuli compete for the associative
strength available for conditioning.

45. RESCORLA-WAGNER THEORY:
CONTINGENCY
 Theory can also explain animals’ ability to detect
different degrees of contingency between CS
and US.
 Recall that fear of a CS for shock is a direct
function of contingency between CS and US.
 When contingency between events is zero, no
learning of fear to CS occurs.
 But, does a rat really compute probabilities to
form a judgment of contingency?
 Not according to Rescorla-Wagner model.

46. RESCORLA-WAGNER THEORY:
CONTINGENCY
 To explain contingency
sensitivity, Rescorla-Wagner
theory makes use of
background or contextual
stimuli as Pavlovian predictors.
(Context = A discrete CS)
 Such contextual stimuli
themselves can compete with
CSs for association with USs.
 Case of random presentations
of CS and US provides a useful
illustration.

47. RESCORLA-WAGNER THEORY:
CONTINGENCY
 Random training can be seen to represent blocking with two kinds of
trials:
 A (context)-US [relatively frequent]
 AX (context plus CS)-US [relatively infrequent]
 As animal receives frequent A-US pairings, VA (and hence VAX)
approaches asymptote.
 As VAX approaches asymptote from frequent A-US pairings, VX can
receive no further increments and little responding to X will be
observed despite occasional AX-US pairings.
CS
unpaired
US
0.5 s
time

48. RESCORLA-WAGNER THEORY:
CONTINGENCY
 So, blocking is basic to effect of random CS and
US presentations.
 Contextual cues are present whenever US
occurs in absence of CS; contextual cues thus
acquire excitatory strength.
 On trials when CS is paired with US by chance,
contextual cues are present as well.
 So, context replaces Stimulus A in blocking
example and randomly presented CS replaces
Stimulus X.

49. RESCORLA-WAGNER THEORY:
INHIBITION
 In Chapter 4, we saw that conditioning can be
either excitatory or inhibitory.
 At first glance, it is not obvious that RescorlaWagner theory can explain inhibition.
 Inhibition requires a V that is less than zero; but,
none of the variables in the equation can ever
be less than zero.
How can V become negative when
none of the terms contributing to V
can be negative?

50. Time to Leave:

51. Y Axis
1
Zero 0
X Axis