Human sensitivity to reinforcement feedback functions

Two experiments investigated human sensitivity to the temporally extended aspects of reinforcement schedules. Experiment 1 investigated human sensitivity to the extended and local aspects of three reinforcement schedules: variable ratio (VR), variable interval (VI), and variable-interval-plus-linear-feedback (VI+) schedules. Experiment 2 investigated this sensitivity on two reinforcement schedules: VI and VI+ schedules. In both experiments, there was evidence of sensitivity to the temporally extended aspects of the schedule: There were differences between the response rate on the VI+ and yoked-VI schedules, but no statistical difference in rates of response between the VR and VI+ schedules. The VI+ versus VI difference was much more pronounced when a lower response force needed to depress a lever was used. These results suggest that human subjects do show some sensitivity to temporally extended aspects of schedules of reinforcement.     

Effects of fixed and variable ratios on human behavioral variability.

The effect that ratio schedules of reinforcement had upon variability of responding was investigated in college students. Subjects were paid $0.02 contingent upon completion of eight presses, distributed in any combination across two push buttons; 256 different sequences were possible. Sequence emission was reinforced according to fixed- and variable-ratio schedules. Ratio requirements of 1, 2, 4 and 8 were presented in alternate components of a multiple schedule. The variability engendered by variable-ratio schedules was also compared to that engendered by fixed ratios. Variability increased with ratio size, irrespective of whether the schedule requirement was fixed or variable. The data demonstrate the similarity between the determinants of human and nonhuman variability, and they illustrate the role of ratio size in determining variability in operant behavior.     

A comparison of ratio and interval reinforcement schedules with comparable interreinforcement times

Pigeons were trained to peck keys on fixed-ratio and fixed-interval schedules of food reinforcement. Both schedules produced a pattern of behavior characterized as pause and run, but the relation of pausing to time between reinforcers differed for the two schedules even when mean time between reinforcers was the same. Pausing in the fixed ratio occupied less of the time between reinforcers for shorter interreinforcer times. For two of three birds, the relation was reversed at longer interreinforcer times. As an interreinforcer time elapsed, there was an increasing tendency to return to responding for the fixed interval, but a roughly constant tendency to return to responding for the fixed-ratio schedule. In Experiment 1 these observations were made for both single-reinforcement schedules and multiple schedules of fixed-ratio and fixed-interval reinforcement. In Experiment 2 the observations were extended to a comparison of fixed-ratio versus variable-interval reinforcement schedules, where the distribution of interreinforcement times in the variable interval approximated that for the fixed ratio.     

Response elimination in rats with schedules of omission training, including yoked and response-independent reinforcement comparisons

After rats were trained to lever press, response elimination began with factorial combinations of fixed vs variable and adjusting vs constant omission training schedules. A time interval scheduling reinforcement remained the same in a constant schedule, and its length was increased as response rate declined in the adjusting schedule. A variable time (VT) response-independent reinforcement schedule followed response elimination to test the durability of response cessation. Experiment I included groups whose reinforcement was yoked to that received by the omission schedule groups. Rate of response elimination was faster with an adjusting than a constant schedule, and slightly faster with a variable than a fixed schedule. There were no significant differences in rate of response elimination between omission schedule and yoked groups. Shorter delay of reinforcement tended to increase rate of response elimination. In the subsequent VT durability test all groups displayed near-zero response rates. In Experiment II adjusting fixed and variable omission schedules, including yoked groups, were compared with fixed time (FT) and VT reinforcement schedules. Response elimination was slower in the FT and VT groups, and they responded more in a subsequent VT durability test. It was concluded that differential reinforcement of other behavior fails to account for these omission training effects, and suggestions were made for an analysis based on the correlation between response and reinforcement rate.     

Rate dependent effects of imipramine: Effects of imipramine on operant behaviour in rats at various levels of water deprivation

The behavioural effects of 1.0, 3.10 and 6.0 mg/kg imipramine injections on lever pressing of rats were studied. Lever pressing was reinforced according to a continuous reinforcement schedule at 0, 24, and 48 h of water deprivation, according to fixed ratio schedules with 22 1/2 h of water deprivation, and according to differential-reinforcement-of-low-rate schedules with 22 1/2 h of water deprivation. The mean rate of responding per min increased significantly at 1.0 mg/kg on the continuous reinforcement schedule at 24 h of deprivation. Otherwise, a dose-related significant reduction in the mean response rate per min occurred on the fixed raito schedules and partly on the differential-reinforcement-of-low-rate schedules, thus lending support to the idea that rate dependent effects may be produced only on schedules of reinforcement such as the fixed ratio, the fixed interval and the variable interval. The results also indicate that depenent effects may be produced only at moderate levels of water deprivation. Some critical comments are made on concepts of rate dependency in view of the results and of previous finding.     

Performance in concurrent interval schedules: a systematic replication

Five pigeons were trained on a variety of concurrent interval schedules that arranged reinforcements at either fixed or variable times after the last reinforcement. Two measures were obtained: the number of responses on each schedule, and the time spent responding on each schedule. Ratios of response rates on the two schedules did not equal ratios of reinforcement rates when both schedules were variable nor when one was variable and the other fixed. Ratios of times spent responding approximately equalled ratios of reinforcement rates when both schedules were variable, but did not do so when one was fixed.     

Molar And Molecular Control In Variable-interval And Variable-ratio Schedules

Response rates are typically higher under variable-ratio than under variable-interval schedules of reinforcement, perhaps because of differences in the dependence of reinforcement rate on response rate or because of differences in the reinforcement of long interresponse times. A variable-interval-with-added-linear-feedback schedule is a variable-interval schedule that provides a response rate/reinforcement rate correlation by permitting the minimum interfood interval to decrease with rapid responding. Four rats were exposed to variable-ratio 15, 30, and 60 food reinforcement schedules, variable-interval 15-, 30-, and 60-s food reinforcement schedules, and two versions of variable-interval-with-added-linear-feedback 15-, 30-, and 60-s food reinforcement schedules. Response rates on the variable-interval-with-added-linear-feedback schedule were similar to those on the variable-interval schedule; all three schedules led to lower response rates than those on the variable-ratio schedules, especially when the schedule values were 30. Also, reinforced interresponse times on the variable-interval-with-added-linear-feedback schedule were similar to those on variable interval and much longer than those produced by variable ratio. The results were interpreted as supporting the hypothesis that response rates on variable-interval schedules in rats are lower than those on comparable variable-ratio schedules, primarily because the former schedules reinforce long interresponse times.     

The schedule dependency of the signaled reinforcement effect

In Experiment 1, rats leverpressed for food reinforcement on either a variable ratio (VR) 30 schedule or a variable interval (VI) 15-s schedule. One group in each condition received a signal filling a 500-ms delay of reinforcement. This treatment enhanced rates on the VR schedule, and attenuated rates on the VI schedule, relative to the rate seen in an unsignaled control condition. In Experiment 2 there was no delay of reinforcement and the signal and food were presented simultaneously. Attenuated rates of responding were observed on VI schedules with a range of mean interval values (15 to 300 s). Experiment 3 used a range of VR schedules (10 to 150) with simultaneous presentations of signal and food. A signal-induced enhancement of response rate was found at all VR values. In Experiment 4, a signal elevated response rates on a tandem VI VR schedule, but depressed rates on a tandem VR VI schedule, compared to control conditions receiving unsignaled delayed reinforcement. These results are taken to show that the effect of a signal accompanying reinforcement depends upon the nature of the behavior that is reinforced during exposure to a given schedule.     

Human choice in "counterintuitive" situations: fixed- versus progressive-ratio schedules.

College undergraduates were given repeated opportunities to choose between a fixed-ratio and a progressive-ratio schedule of reinforcement. Completions of a progressive-ratio schedule produced points (exchangeable for money) and incremented that response requirement by 20 responses with each consecutive choice. In the reset condition, completion of a fixed ratio produced the same number of points and also reset the progressive ratio back to its initial value. In the no-reset condition, the progressive ratio continued to increase by increments of 20 throughout the session with each successive selection of this schedule, irrespective of fixed-ratio choices. Subjects' schedule choices were sensitive to parametric manipulations of the size of the fixed-ratio schedule and were consistent with predictions made on the basis of minimizing the number of responses emitted per point earned, which is a principle of most optimality theories. Also, the present results suggest that if data from human performances are to be compared with results for other species, humans should be exposed to schedules of reinforcement for long periods of time, as is commonly done with nonhuman subjects.     

Response rate and sensitivity to the molar feedback function relating response and reinforcement rate on VI+ schedules of reinforcement

In 5 experiments, the author examined rats' sensitivity to the molar feedback function relating response rate to reinforcement rate on schedules of reinforcement. These studies demonstrated that, at lower rates of responding, rats' performance on variable ratio (VR), variable interval (VI), and variable interval with linear feedback loop (VI+) schedules was determined largely by reinforcement of interresponse times; response rates were faster on VR than on both VI and VI+ schedules. In contrast, when procedures were adopted to maintain high rates of response, rats showed sensitivity to the molar characteristics of the schedules; they responded as fast on a VI+ schedule as on a VR schedule and faster on both of these schedules than on a yoked VI schedule. When the variance of response rate was manipulated, this factor was noted as an important element in determining sensitivity to the molar characteristics of the schedule.     

Fixed and variable ratios and delays: further tests of an equivalence rule

A discrete-trial procedure was used to measure pigeons' choices between fixed and variable ratio schedules and between fixed and variable delays before reinforcement. A peck at a green key produced a reinforcement schedule that was constant within a condition but varied across conditions. A peck at a red key produced a ratio schedule (or, in other conditions, a simple delay) whose size was increased or decreased many times a session, depending on the subject's previous choices. The purpose of these adjustments was to estimate an indifference point--a ratio size (or delay duration) at which the subject chose each key about equally often. The results were used to test a simple "equivalence rule" for choices between fixed and variable schedules (Mazur, 1984). This rule, which was applied without using free parameters, predicted the major trends in the obtained indifference points from both ratio and delay conditions. However, some small but consistent deviations from the predictions were apparent. Better predictions were generated with a more complex equation, which included parameters reflecting the subjects' sensitivities to delay of reinforcement and to events of different probabilities. It was concluded that a successful equivalence rule must include parameters that can be adjusted to describe the effects of delay and probability in a given experimental setting. Once these parameters are estimated, however, choices involving both fixed and variable delays and fixed and variable ratios can be accurately predicted with the same equation.     

Tolerance to effects of cocaine on behavior under a response-initiated fixed-interval schedule

Tolerance to effects of cocaine can be modulated by schedules of reinforcement. With multiple ratio schedules, research has shown an inverse relationship between ratio requirement and amount of tolerance that resulted from daily administration of the drug. In contrast, tolerance to the effects of cocaine on behavior under multiple interval schedules generally has developed regardless of interval value. Under interval schedules reinforcement depends on the animal making one response following a time interval. Thus, as time to respond increases, the time to reinforcement decreases. On the other hand, fixed ratio schedules require a specified number of responses to be made prior to reinforcement. Therefore, delaying the initiation of responding does not coincide with a significant decrease in the time to reinforcement. In the current experiment, 6 pigeons were trained to respond under a three-component multiple schedule, with a different tandem fixed-ratio 1 fixed-interval schedule in each component. The multiple schedule required one response, which was followed by one of three fixed-interval values (5, 15, or 60 s). Thus, the multiple schedule was interval-like because after the fixed-ratio 1, only one more response was required for reinforcement, but it was also ratio-like because the length of the pause at the beginning of each interreinforcer interval affected the time until the next reinforcer. Acute administration of cocaine generally resulted in dose-dependent decreases in responding. Chronic (i.e., daily) administration of a rate-decreasing dose resulted in tolerance patterns similar to those usually obtained with multiple ratio schedules. That is, the magnitude of tolerance was related inversely to schedule size. These results suggest that delay to reinforcement from the initial response may play a role in the development of schedule-parameter-related tolerance.     

Effects of Attribution and Schedules of Reinforcement on Performance

Abstract

We examined the impact of attributional instructions and schedules of reinforcement on performance. Attributional instructions were designed to lead to an internal or an external attribution, whereas schedules of reinforcement were either variable ratio or variable interval. Results obtained from 31 American students indicated that the subjects given external attributional instructions made a greater number of responses but did not respond more correctly. The schedule of reinforcement did not influence either the number of responses or the correctness of responses.     

DISCRIMINATION OF VARIABLE SCHEDULES IS CONTROLLED BY INTERRESPONSE TIMES PROXIMAL TO REINFORCEMENT

In Experiment 1, food‐deprived rats responded to one of two schedules that were, with equal probability, associated with a sample lever. One schedule was always variable ratio, while the other schedule, depending on the trial within a session, was: (a) a variable‐interval schedule; (b) a tandem variable‐interval, differential‐reinforcement‐of‐low‐rate schedule; or (c) a tandem variable‐interval, differential‐reinforcement‐of‐high‐rate schedule. Completion of a sample‐lever schedule, which took approximately the same time regardless of schedule, presented two comparison levers, one associated with each sample‐lever schedule. Pressing the comparison lever associated with the schedule just presented produced food, while pressing the other produced a blackout. Conditional‐discrimination accuracy was related to the size of the difference in reinforced interresponse times and those that preceded it (predecessor interresponse times) between the variable‐ratio and other comparison schedules. In Experiment 2, control by predecessor interresponse times was accentuated by requiring rats to discriminate between a variable‐ratio schedule and a tandem schedule that required emission of a sequence of a long, then a short interresponse time in the tandem's terminal schedule. These discrimination data are compatible with the copyist model from Tanno and Silberberg (2012) in which response rates are determined by the succession of interresponse times between reinforcers weighted so that each interresponse time's role in rate determination diminishes exponentially as a function of its distance from reinforcement.     

Titration of schedule parameters by pigeons

Pigeons were tested in a computer-controlled two-key chamber. A standard (nonchanging) schedule of reinforcement was in force on one key, and an adjusting schedule on the other. The schedules were available concurrently after each reinforcement, but after the first peck on either key (the choice peck), the schedule on the other key was made inoperative. The parameter of the adjusting schedule was decreased when the standard schedule was chosen and increased when the adjusting schedule was chosen. The standard schedule was changed only between sessions. Fixed intervals and fixed ratios were used as standard schedules, and intervals and ratios were used as adjusting schedules. When standard and adjusting schedules were of the same type, median parameters on the adjusting key equalled those of the standard schedules, at four values of each standard schedule. For four of five birds, and for the group median, similar curves could be plotted through the indifference points obtained from a standard ratio with an adjusting interval, and from a standard interval with an adjusting ratio. These points showed consistent individual differences, but they could be predicted by assuming that the median time from the choice peck to reinforcement should be the same on both keys. This is equivalent to treating the schedule as a concurrent chain and assuming that Herrnstein's quantitative law of effect applies.     

Optimal behavior and concurrent variable ratio-variable interval schedules

Concurrent variable ratio-variable interval (CONC VRVI) schedules of reinforcement, and the time-based analog of the same schedule (CONC VT*VT), have been used to determine if the matching law accounts for the distribution of choices between the behavior alternatives more accurately than the assumption that subjects distribute time between the alternatives to maximize total reinforcement rate. The results of those experiments leave room for interpretation. One problem is the lack of understanding of the theoretical outcomes associated with maximization in these schedules. A precise understanding of the characteristics of optimal behavior (OB) could help identify experimental evidence of OB. Here we derive equations that describe the optimal times the subject should spend on each alternative of the schedule. We provide a table of the optimal times for a wide range of parameter values of the schedule that experimenters can use to compare easily experimental results to the results expected if subjects behave optimally. We also derive a function m that relates matching and optimal performance and we prove interesting characteristics of the function. Finally, we describe features of OB with CONC VT*VT and with concurrent variable time schedules that can be used to identify evidence of OB.     

Children's preference for mixed‐ versus fixed‐ratio schedules of reinforcement: A translational study of risky choice

Laboratory research has shown that when subjects are given a choice between fixed‐ratio and bi‐valued mixed‐ratio schedules of reinforcement, preference typically emerges for the mixed‐ratio schedule even with a larger ratio requirement. The current study sought to replicate and extend these findings to children's math problem completion. Using an ABCBC reversal design, four fourth‐grade students were given the choice of completing addition problems reinforced on either a fixed‐ratio 5 schedule or one of three mixed‐ratio schedules; an equivalent mixed‐ratio (1, 9) schedule, a mixed‐ratio (1, 11) schedule with a 20% larger ratio requirement, and an equally lean mixed‐ratio (5, 7) schedule without the small fixed‐ratio 1 component. This was followed by a reversal back to the preceding phase in which preference for the mixed‐ratio schedule had been observed, and a final reversal back to the mixed‐ratio (5, 7) phase. Findings were consistent with previous research in that all children preferred the mixed‐ratio (1, 9) schedule over the equivalent fixed‐ratio 5 schedule. Preference persisted for the leaner mixed‐ratio (1, 11) schedule for three of the four children. Indifference or preference for the fixed‐ratio 5 alternative was observed in phases containing the mixed‐ratio (5, 7) schedule. These results extend previous research on risky choice to children's math problem completion and highlight the importance of a small ratio component in the emergence of preference for bi‐valued mixed‐ratio schedules. Implications of these results for arranging reinforcement to increase children's academic responding are discussed.     

Ratio reinforcement of matching behavior

Three pigeons, previously trained to a high level of accuracy on matching-to-sample procedures, were exposed to various schedules of ratio reinforcement for correct matches. Overall accuracy was lower on fixed ratio than on regular reinforcement. There was a high incidence of errors immediately after reinforcement on fixed ratio schedules with accuracy increasing as the ratio progressed. This increase was found to be inversely correlated with the latency of the observing response to the sample. By contrast, accuracy was high throughout the ratio on a variable ratio schedule.     

Observational learning in monkeys

Observer monkeys were housed next to demonstrator monkeys that were conditioned to respond on a multiple reinforcement schedule whose components were fixed-ratio 32, variable-interval 3-min, and extinction 5-min followed by an additional 30 sec of extinction during which every response started a new 30-sec interval. After observational periods from 113 to 210 hr long, during which observers could not perform the response and were given no extrinsic reinforcers, their first-response latencies to fixed ratio and variable interval were as short as the demonstrators; and their rates of responding were well above pre-observational baseline levels. About 8 hr later, a temporal pattern of responding appropriate to the multiple schedule emerged, including non-emission of responses during extinction. Controls lacking the chance to observe did not develop typically patterned responding after 60 hr in one case and, in two other cases, after 80 hr during which, on two occasions, every one of 50 responses was reinforced. In a second experiment, the stimulus lights associated with fixed ratio and variable interval were presented simultaneously. Subjects chose one of the schedules by responding to one of the levers beneath the lights. All subjects initially chose fixed ratio. Seeing the demonstrators switch to variable interval, due to increases in the fixed-ratio requirement, had no effect upon observers, which continued to choose fixed ratio.