Rescorla-Wagner (1972) Theory of Classical Conditioning

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Rescorla-Wagner (1972) Theory of Classical Conditioning

HISTORY Ever since Pavlov, it was assumed that any CS followed contiguously by any US would result in conditioning. Not true: Contingency Not true: Taste Aversion Learning Not true: Blocking

Rescorla-Wagner Theory (1972) Emerged from Kamin s work on blocking Organisms only learn when events violate their expectations If a US is surprising, the organism searches its memory for possible causes. If a US is expected, then an adequate predictor must be already available; no memory search occurs and no new learning takes place. These expectations are modified only when consequent events disagree with the composite expectation Expectations are the key!

The concepts of Rescorla and Wagner The precise amount of conditioning is dependent upon the amount of surprise. Surprise not only determines whether conditioning occurs but also how strong it is. In mathematical words 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 = 1 (number is arbitrary & based on the strength of the UCS) Vall = (because no conditioning has occurred) Vcs = (no conditioning has occurred yet) c =.5 (c must be a number between and 1. and is a result of dividing the CS intensity by the UCS intensity)

First Conditioning Trial 1.5 * 1 - = 5 1 Associative Strength (V) 8 6 4 2 5 Vall 1 2 3 4 5 6 7 8

Second Conditioning Trial 2.5 * 1-5 = 25 1 Associative Strength (V) 8 6 4 2 5 75 Vall 1 2 3 4 5 6 7 8

Third Conditioning Trial 3.5 * 1-75 = 12.5 1 87.5 Associative Strength (V) 8 6 4 2 5 75 Vall 1 2 3 4 5 6 7 8

4th Conditioning Trial 4.5 * 1-87.5 = 6.25 Associative Strength (V) 1 8 6 4 2 93.75 87.5 75 5 Vall 1 2 3 4 5 6 7 8

5th Conditioning Trial 5.5 * 1-93.75 = 3.125 Associative Strength (V) 1 8 6 4 2 75 5 87.5 93.7596.88 Vall 1 2 3 4 5 6 7 8

6th Conditioning Trial 6.5 * 1-96.88 = 1.56 Associative Strength (V) 1 8 6 4 2 75 5 87.5 93.7596.8898.44 Vall 1 2 3 4 5 6 7 8

7th Conditioning Trial 7.5 * 1-98.44 =.78 Associative Strength (V) 1 8 6 4 2 75 5 87.5 93.7596.8898.44 99.22 Vall 1 2 3 4 5 6 7 8

8th Conditioning Trial 8.5 * 1-99.22 =.39 Associative Strength (V) 1 8 6 4 2 87.5 75 5 93.75 96.8898.44 99.2299.61 Vall 1 2 3 4 5 6 7 8

1st Extinction Trial 1.5 * - 99.61 = -49.8 Extinction Associative Strength (V) 1 8 6 4 2 99.61 49.8 Vall 1 2 3 4 5 6

2nd Extinction Trial 2.5 * - 49.8 = -24.9 Extinction Associative Strength (V) 1 8 6 4 2 99.61 49.8 24.9 Vall 1 2 3 4 5 6

Extinction 3.5 * - 12.45 = -12.46 4.5 * - 6.23 = -6.23 5.5 * - 3.11 = -3.11 6.5 * - 1.56 = -1.56

Hypothetical Acquisition & Extinction Curves with c=.5 and Vmax = 1 Acquisition Extinction Associative Streng th (V ) 1 8 6 4 2 93.75 96.8898.44 99.2299.61 87.5 75 5 Vall 1 2 3 4 5 6 7 8 A ssoci a tive Stre n g th ( V ) 1 8 6 4 2 99.61 49.8 24.9 12.45 6.23 Vall 3.11 1.56 1 2 3 4 5 6

Acquisition & Extinction Curves with c=.5 vs. c=.2 (Vmax = 1) Acquisition Extinction Associative Strength (V) 12 1 8 6 4 2 1 2 3 4 5 6 7 8 Associative Strength (V) 12 1 8 c=.5 6 c=.2 4 2 1 2 3 4 5 6 c=.5 c=.2

Conditioning can reach different strengths at different rates

Theory Handles other Phenomena: compound conditioning Overshadowing Whenever there are multiple stimuli or a compound stimulus, then Vall = Vcs 1 + Vcs 2 Trial 1: Vnoise =.2 (1 ) = (.2)(1) = 2 Vlight =.3 (1 ) = (.3)(1) = 3 Total Vall= current Vall + Vnoise + Vlight = +2 +3 =5 Trial 2: Vnoise =.2 (1 5) = (.2)(5) = 1 Vlight =.3 (1 5) = (.3)(5) = 15 Total Vall= current Vall + Vnoise + Vlight = 5+1+15=75

Other Phenomena: Blocking effect Va = c(vmax Vab) Vb = c(vmax Vab) where Vab = Va+ Vb; c =.5 Trial Vn Vn = c(vmax - Vn) 1. V =.5(1 -.) =.5 2.5 V =.5(1 -.5) =.25 3.75 V =.5(1 -.75) =.13 4.88 V =.5(1 -.88) =.6 5.94 V =.5(1 -.94) =.3 6.97 V =.5(1 -.97) =.2 7.99 V =.5(1 -.99) =.1 8 1. V =.5(1 1.) =. 9 1. V =.5(1 1.) =. 1 1. V =.5(1 1.) =.

Vn Va = c(vmax Vab) Vb = c(vmax Vab) 1 Va 1..5(1-1.) =. 1 Vb..5(1-1.) =. 2 Va 1..5(1-1.) =. 2 Vb..5(1-1.) =. 3 Va 1..5(1-1.) =. 3 Vb..5(1-1.) =. 4 Va 1..5(1-1.) =. 4 Vb..5(1-1.) =. 5 Va 1..5(1-1.) =. 5 Vb..5(1-1.) =. Blocking Vn 1.8.6.4.2 1 3 5 7 9 11 13 15 17 19 Va Vb

Theory Handles other Phenomena Overexpectation Effect: the victory of the model! Separately condition two simple CS's until both are fully conditioned for the first time, present the two together as a compound CS Expect 2% of associative value (twice the reward) the model predicts that, as the compound is paired with the US trial after trial, the associative value of the compound CS will actually decrease until it reaches the same maximum that a simple CS would sustain

Conceptual problems with the Rescorla-Wagner model V represents the strength of a theoretical association (not a real one). How do we relate measures of overt behavior to associative strength? We need to know the values of c and Vmax before we can predict V. How do we do that? Solution = it is not necessary to know the exact values to test the model; use arbitrary values instead. The use of arbitrary values will not allow us to make precise quantitative predictions. For example, we cannot predict how many drops of saliva will occur after 2 pairings of a TONE (CS) with a FOOD (US). The use of arbitrary values will allow us to make qualitative predictions. For example, we can predict whether the amount of saliva will increase or decrease over trials.

What is missing? A major parameter left out of the model is time. All changes take place as a function of trials, and although trials follow themselves in time, such parameters as the length of a CS presentation, time between US presentations, or duration of a trace interval are not explicitly included in the Rescorla- Wagner model. As these factors have strong effects on the course of conditioning, their absence from the model was always a serious limitation.

Rescorla-Wagner Model The theory is not perfect But, it has been the best theory of Classical Conditioning

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