Solution of the comparator theory of associative learning.

Abstract

We derive an analytical solution of the comparator theory of associative learning, as formalized by Stout and Miller (2007). The solution enables us to calculate exactly the predicted responding to stimuli in any experimental design and for any choice of model parameters. We illustrate its utility by calculating the predictions of comparator theory in some paradigmatic designs: acquisition of conditioned responses, compound conditioning, blocking, unovershadowing, and backward blocking. We consider several versions of the theory: first-order comparator theory (close to the original ideas of Miller & Matzel, 1988), second-order comparator theory (Denniston, Savastano, & Miller, 2001), and sometimes-competing retrieval (Stout & Miller, 2007). We show that all versions of comparator theory make a number of surprising predictions, some of which appear hard to reconcile with empirical data. Our solution paves the way for a fuller understanding of the theory and for its empirical evaluation.

Beyond Rescorla–Wagner: the Ups and Downs of Learning

“…Clear examples of response fluctuations are shown in Fig. 6 of Ghirlanda and Ibadullaiev (2015), which reproduces, among others, results of Miller et al (1981) and Zelikowsky and Fanselow (2010). In particular, the data from Miller et al (1981) show fluctuations in response rates above and below the idealized acquisition curve, while the data from Zelikowsky and Fanselow (2010) show a clear overshoot in initial responding that is corrected in later trials.…”

A response function that maps associative strengths to probabilities.

“…Equation 1 is not the only proposal to quantify the assumption that responding is an increasing function of associative strength (Rescorla & Wagner, 1972). A linear function fits some data well (Ghirlanda & Ibadullaiev, 2015; Thein et al, 2008), but ultimately a nonlinear function appears necessary to accommodate response ceilings, subadditive summation such as in Equation 2, and other findings. For example, the data in Rescorla (2000) suggest that, in violation of the Rescorla and Wagner (1972) learning equation, a trial with AB may result in unequal changes to V A and V B , even when the two CSs have equal salience.…”

A double error dynamic asymptote model of associative learning.

“…That is, the B→US link is relatively larger than the A→US link after the latter has lost associative strength in the second phase. However, a formal analysis of various comparator models has cautioned that such revaluation effects might be harder to reproduce than originally conjectured (Ghirlanda & Ibadullayev, 2015, p. 18). Though the TD model does not presume learning between neutral stimuli, the Predictive Representations (Ludvig & Koop, 2008) extension of it accounts for mediated conditioning by proposing that present cues retrieve representations of stimuli with which they have been previously presented.…”