Editing Classical conditioning (section)

===Rescorla–Wagner model===
{{main|Rescorla–Wagner model}}

The Rescorla–Wagner (R–W) model<ref name="Bouton_2016"/><ref>{{cite book |vauthors=Rescorla RA, Wagner AR |date=1972 |chapter=A theory of Pavlovan conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. |title=Classical Conditioning II: Current Theory and Research |chapter-url=https://archive.org/details/classicalconditi0000unse |chapter-url-access=registration |veditors=Black AH, Prokasy WF |pages=[https://archive.org/details/classicalconditi0000unse/page/64 64–99] |location=New York |publisher=Appleton-Century}}</ref> is a relatively simple yet powerful model of conditioning. The model predicts a number of important phenomena, but it also fails in important ways, thus leading to a number of modifications and alternative models. However, because much of the theoretical research on conditioning in the past 40 years has been instigated by this model or reactions to it, the R–W model deserves a brief description here.<ref name="M&E">{{cite book |vauthors=Miller R, Escobar M |chapter=Learning: Laws and Models of Basic Conditioning |title=Stevens' Handbook of Experimental Psychology |edition=3rd |volume=3: Learning, Motivation & Emotion |veditors=Pashler H, Gallistel R |pages=47–102 |location=New York |publisher=Wiley |isbn=978-0-471-65016-4 |date=2004-02-05}}</ref><ref name="Chance_2008" />{{rp|85}}

The Rescorla-Wagner model argues that there is a limit to the amount of conditioning that can occur in the pairing of two stimuli. One determinant of this limit is the nature of the US. For example: pairing a bell with a juicy steak is more likely to produce salivation than pairing the bell with a piece of dry bread, and dry bread is likely to work better than a piece of cardboard. A key idea behind the R–W model is that a CS signals or predicts the US. One might say that before conditioning, the subject is surprised by the US. However, after conditioning, the subject is no longer surprised, because the CS predicts the coming of the US. (The model can be described mathematically and that words like predict, surprise, and expect are only used to help explain the model.) Here the workings of the model are illustrated with brief accounts of acquisition, extinction, and blocking. The model also predicts a number of other phenomena, see main article on the model.

====Equation====
<math display="block">\Delta V=\alpha\beta (\lambda - \Sigma V)</math>

This is the Rescorla-Wagner equation. It specifies the amount of learning that will occur on a single pairing of a conditioning stimulus (CS) with an unconditioned stimulus (US). The above equation is solved repeatedly to predict the course of learning over many such trials.

In this model, the degree of learning is measured by how well the CS predicts the US, which is given by the "associative strength" of the CS. In the equation, V represents the current associative strength of the CS, and ∆V is the change in this strength that happens on a given trial. ΣV is the sum of the strengths of all stimuli present in the situation. λ is the maximum associative strength that a given US will support; its value is usually set to 1 on trials when the US is present, and 0 when the US is absent. α and β are constants related to the salience of the CS and the speed of learning for a given US. How the equation predicts various experimental results is explained in following sections. For further details, see the main article on the model.<ref name="Chance_2008" />{{rp|85–89}}

====R–W model: acquisition====
The R–W model measures conditioning by assigning an "associative strength" to the CS and other local stimuli. Before a CS is conditioned it has an associative strength of zero. Pairing the CS and the US causes a gradual increase in the associative strength of the CS. This increase is determined by the nature of the US (e.g. its intensity).<ref name="Chance_2008" />{{rp|85–89}} The amount of learning that happens during any single CS-US pairing depends on the difference between the total associative strengths of CS and other stimuli present in the situation (ΣV in the equation), and a maximum set by the US (λ in the equation). On the first pairing of the CS and US, this difference is large and the associative strength of the CS takes a big step up. As CS-US pairings accumulate, the US becomes more predictable, and the increase in associative strength on each trial becomes smaller and smaller. Finally, the difference between the associative strength of the CS (plus any that may accrue to other stimuli) and the maximum strength reaches zero. That is, the US is fully predicted, the associative strength of the CS stops growing, and conditioning is complete.

====R–W model: extinction====
[[File:Rescorla–Wagner model in Learning.svg|thumb|Comparing the associate strength by R-W model in Learning]]
The associative process described by the R–W model also accounts for extinction (see "procedures" above). The extinction procedure starts with a positive associative strength of the CS, which means that the CS predicts that the US will occur. On an extinction trial the US fails to occur after the CS. As a result of this "surprising" outcome, the associative strength of the CS takes a step down. Extinction is complete when the strength of the CS reaches zero; no US is predicted, and no US occurs. However, if that same CS is presented without the US but accompanied by a well-established conditioned inhibitor (CI), that is, a stimulus that predicts the absence of a US (in R-W terms, a stimulus with a negative associate strength) then R-W predicts that the CS will not undergo extinction (its V will not decrease in size).

====R–W model: blocking====
{{main|Blocking effect}}
The most important and novel contribution of the R–W model is its assumption that the conditioning of a CS depends not just on that CS alone, and its relationship to the US, but also on all other stimuli present in the conditioning situation. In particular, the model states that the US is predicted by the sum of the associative strengths of all stimuli present in the conditioning situation. Learning is controlled by the difference between this total associative strength and the strength supported by the US. When this sum of strengths reaches a maximum set by the US, conditioning ends as just described.<ref name="Chance_2008" />{{rp|85–89}}

The R–W explanation of the blocking phenomenon illustrates one consequence of the assumption just stated. In blocking (see "phenomena" above), CS1 is paired with a US until conditioning is complete. Then on additional conditioning trials a second stimulus (CS2) appears together with CS1, and both are followed by the US. Finally CS2 is tested and shown to produce no response because learning about CS2 was "blocked" by the initial learning about CS1. The R–W model explains this by saying that after the initial conditioning, CS1 fully predicts the US. Since there is no difference between what is predicted and what happens, no new learning happens on the additional trials with CS1+CS2, hence CS2 later yields no response.