Rescorla Wagner model

The Rescorla-Wagner model is a mathematical model designed to make classical conditioning and some of its most important effects predictable. The basic assumption of the model is that a stimulus can only serve as a good predictor for predicting effects if it is surprising. It was presented in 1972 by Robert A. Rescorla and Allan R. Wagner and still has a permanent place in educational psychology today - although it has since been modified and expanded.

Basics

In classical conditioning , an organism (test person or test animal) is repeatedly presented with an unconditioned stimulus (US) and a conditioned stimulus (CS), usually at short intervals, one after the other or overlapping. The organism, which previously only showed a reaction to the US (unconditioned reaction, UR), shows a similar reaction (conditioned reaction, CR) after a few repetitions, even when the conditioned stimulus is presented alone.

In classical conditioning, a distinction is made between acquisition and extinction runs :

Acquisition (acquisition). An unconditioned and conditioned stimulus (CS / US) are presented together . The probability with which the organism will show a conditioned reaction to the conditioned stimulus increases with each cycle - at the beginning very strongly and later with a decreasing slope towards an asymptotic maximum.
Extinction (extinction). The conditioned stimulus is presented alone. The probability with which the organism shows a conditioned reaction to the conditioned stimulus decreases with each cycle until finally no conditioned reaction at all to the originally conditioned stimulus is shown.

The importance of the Rescorla-Wagner model

Before the Rescorla-Wagner model, attempts were made several times in vain to design a mathematical model that predicts the probability with which an organism will show the conditioned response to the conditioned stimulus. Although all of them were able to explain the basic form of classical conditioning, they failed because of the explanation of conditioning with more than two stimuli or the prediction of special effects. The Rescorla-Wagner model was not only the first that could mathematically explain all previously known effects, it could also predict new effects.

The model not only correctly predicts the usual classical conditioning with one or more conditioned stimuli, but also makes the following effects predictable in particular:

Phenomena such as latent inhibition , configural cues (including configuration learning), spontaneous recovery and associative bias are problematic for the model .

The formula

The Rescorla-Wagner model culminates in the mathematical equation:

{\ displaystyle \ Delta V_ {A (n)} = \ alpha _ {A} \ cdot \ beta _ {US (n)} \ cdot \ left (\ lambda _ {US (n)} - V_ {all (n )} \ right)}

The individual variables have the following meanings and value ranges:

A is the conditioned stimulus (CS), or one of the conditioned stimuli, if there are several. A can be replaced with more meaningful words; For example, you could write for a specific application of the formula . ${\ displaystyle \ Delta V_ {Light stimulus (s)}}$
n is the number of conditioning passes. Thus, n can be any natural number of any size - including zero.
V is the association strength , so the strength of the associative link between a conditioned stimulus (CS) and the unconditioned stimulus (US). V is not a mathematical measure of probability, as V can also take negative values. V therefore only describes the strength of association between two stimuli, not the probability with which a stimulus triggers a given reaction. Thus:
- ${\ displaystyle V_ {A}}$ the strength of association of the conditioned stimulus A ,

${\ displaystyle \ alpha _ {A}}$ is the learning rate (constant) of stimulus A.

${\ displaystyle \ beta _ {US (n)}}$ is the learning rate (constant) for the unconditioned stimulus.

${\ displaystyle \ lambda _ {US (n)}}$ is the maximum possible strength of association of the US (so-called asymptote )

Put simply, the change in the strength of association depends on the difference between the maximum possible strength of association and the current strength of association : ${\ displaystyle \ Delta V}$ ${\ displaystyle \ lambda}$ ${\ displaystyle V}$

{\ displaystyle \ Delta V = k \ cdot \ left (\ lambda -V \ right)}

So z. For example, you can observe that at the beginning, when this difference is still large, great learning progress is made, while later, when the performance is already close to perfection, only small learning progress is made.

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↑ ^a ^b Rescorla, RA, Wagner, AR (1972). A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. In: AH Black, WF Prokasy (Eds.) Classical conditioning II: Current research and theory. (pp. 64-99). New York: Appleton-Century-Crofts.

[:0-1] Rescorla, RA, Wagner, AR (1972). A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. In: AH Black, WF Prokasy (Eds.) Classical conditioning II: Current research and theory. (pp. 64-99). New York: Appleton-Century-Crofts.