Rescorla-Wagner (1972) Theory of Classical Conditioning

1. Rescorla-Wagner (1972) Theory of Classical Conditioning

2. 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

3. 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

4. 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

5. 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)

6. First Conditioning Trial Trial c(Vmax - Vall) = ∆Vcs 1 .5 * 100 - 0 = 50

7. Second Conditioning Trial Trial c(Vmax - Vall) = ∆Vcs 2 .5 * 100 - 50 = 25

8. Third Conditioning Trial Trial c(Vmax - Vall) = ∆Vcs 3 .5 * 100 - 75 = 12.5

9. 4th Conditioning Trial Trial c(Vmax - Vall) = ∆Vcs 4 .5 * 100 - 87.5 = 6.25

10. 5th Conditioning Trial Trial c(Vmax - Vall) = ∆Vcs 5 .5 * 100 - 93.75 = 3.125

11. 6th Conditioning Trial Trial c(Vmax - Vall) = ∆Vcs 6 .5 * 100 - 96.88 = 1.56

12. 7th Conditioning Trial Trial c(Vmax - Vall) = ∆Vcs 7 .5 * 100 - 98.44 = .78

13. 8th Conditioning Trial Trial c(Vmax - Vall) = ∆Vcs 8 .5 * 100 - 99.22 = .39

14. 1st Extinction Trial Trial c(Vmax - Vall) = ∆Vcs 1 .5 * 0 - 99.61 = -49.8

15. 2nd Extinction Trial Trial c(Vmax - Vall) = ∆Vcs 2 .5 * 0 - 49.8 = -24.9

16. Extinction Trials Trial c(Vmax - Vall) = ∆Vcs 3 .5 * 0 - 12.45 = -12.46 Trial c(Vmax - Vall) = ∆Vcs 4 .5 * 0 - 6.23 = -6.23 Trial c(Vmax - Vall) = ∆Vcs 5 .5 * 0 - 3.11 = -3.11 Trial c(Vmax - Vall) = ∆Vcs 6 .5 * 0 - 1.56 = -1.56

17. Hypothetical Acquisition & Extinction Curves with c=.5 and Vmax = 100

18. Acquisition & Extinction Curves with c=.5 vs. c=.2 (Vmax = 100)

19. 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

20. 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

21. 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