Law of effect models and choice between many alternatives

Quantitative analysis of local-level resurgence

Resurgence is the recurrence of a previously reinforced and then extinguished behavior induced by the extinction of another more recently reinforced behavior. Resurgence provides insight into behavioral processes relevant to treatment relapse of a range of problem behaviors. Resurgence is typically studied across three phases: (1) reinforcement of a target response, (2) extinction of the target and concurrent reinforcement of an alternative response, and (3) extinction of the alternative response, resulting in the recurrence of target responding. Because each phase typically occurs successively and spans multiple sessions, extended time frames separate the training and resurgence of target responding. This study assessed resurgence more dynamically and throughout ongoing training in 6 pigeons. Baseline entailed 50-s trials of a free-operant psychophysical procedure, resembling Phases 1 and 2 of typical resurgence procedures. During the first 25 s, we reinforced target (left-key) responding but not alternative (right-key) responding; contingencies reversed during the second 25 s. Target and alternative responding followed the baseline reinforcement contingencies, with alternative responding replacing target responding across the 50 s. We observed resurgence of target responding during signaled and unsignaled probes that extended trial durations an additional 100 s in extinction. Furthermore, resurgence was greater and/or sooner when probes were signaled, suggesting an important role of discriminating transitions to extinction in resurgence. The data were well described by an extension of a stimulus-control model of discrimination that assumes resurgence is the result of generalization of obtained reinforcers across space and time. Therefore, the present findings introduce novel methods and quantitative analyses for assessing behavioral processes underlying resurgence.

A model for discriminating reinforcers in time and space

Both the response-reinforcer and stimulus-reinforcer relation are important in discrimination learning; differential responding requires a minimum of two discriminably-different stimuli and two discriminably-different associated contingencies of reinforcement. When elapsed time is a discriminative stimulus for the likely availability of a reinforcer, choice over time may be modeled by an extension of the Davison and Nevin (1999) model that assumes that local choice strictly matches the effective local reinforcer ratio. The effective local reinforcer ratio may differ from the obtained local reinforcer ratio for two reasons: Because the animal inaccurately estimates times associated with obtained reinforcers, and thus incorrectly discriminates the stimulus-reinforcer relation across time; and because of error in discriminating the response-reinforcer relation. In choice-based timing tasks, the two responses are usually highly discriminable, and so the larger contributor to differences between the effective and obtained reinforcer ratio is error in discriminating the stimulus-reinforcer relation. Such error may be modeled either by redistributing the numbers of reinforcers obtained at each time across surrounding times, or by redistributing the ratio of reinforcers obtained at each time in the same way. We assessed the extent to which these two approaches to modeling discrimination of the stimulus-reinforcer relation could account for choice in a range of temporal-discrimination procedures. The version of the model that redistributed numbers of reinforcers accounted for more variance in the data. Further, this version provides an explanation for shifts in the point of subjective equality that occur as a result of changes in the local reinforcer rate. The inclusion of a parameter reflecting error in discriminating the response-reinforcer relation enhanced the ability of each version of the model to describe data. The ability of this class of model to account for a range of data suggests that timing, like other conditional discriminations, is choice under the joint discriminative control of elapsed time and differential reinforcement. Understanding the role of differential reinforcement is therefore critical to understanding control by elapsed time.