Maximizing present value: A model to explain why moderate response rates obtain on variable-interval schedules

In Phases 1 and 3, two Japanese monkeys responded on a multiple variable-ratio 80 variable-interval X schedule, where the value of X was adjusted to ensure equal between-schedule reinforcement rates. Components strictly alternated following the delivery of a food pellet, and each session ended following 50 components. Phase 2 differed from the others only in that the 50 pellets previously earned during the session were delivered together at session's end. Variable-ratio response rates did not decrease across phases, but variable-interval response rates decreased substantially during the Phase 2 procedure. This rate decrease was attributed to the food-at-session's-end manipulation removing the greater immediacy of reinforcement provided by short interresponse times relative to long interresponse times. Without this time preference for short interresponse times, the variable-interval interresponse-time reinforcement feedback function largely controlled response emission, dictating a response-rate reduction. This result was explained in terms of the economic notion of “maximizing present value.”     

Signalled reinforcement in differential-reinforcement-of-low rate schedules

At several fixed and variable minimum reinforced interresponse times, a stimulus was added to differential-reinforcement-of-low-rate schedules to signal the availability or nonavailability of reinforcement. As the minimum reinforced interresponse time increased, the rate of unreinforced responding decreased. Changing from fixed to variable minimum interresponse time in the basic differential-reinforcement-of-low-rate schedule further decreased the rate of unreinforced responding. Both effects were to some degree reversible. For fixed minimum reinforced interresponse times of 30 sec or shorter, most unreinforced responses terminated interresponse times just short of that required for reinforcement. The minimum reinforced interresponse time and the number of short response latencies (≤0.5 sec) to the onset of the signal were negatively correlated. Both of these analyses suggested that at values of 30 sec or shorter, the subjects discriminated the availability of the reinforcer more on the basis of time than on the basis of presence or absence of the signal.     

Effects of a DRL contingency added to a fixed-interval reinforcement schedule

Following 30 days of reinforcement for the bar press response of two white rats on 30-sec fixed-interval (FI), a DRL component was added so that a minimal interresponse time (IRT) for the reinforced response, in addition to the FI variable, was necessary for reinforcement. Marked control over response rate by the superimposed DRL requirement was demonstrated by an inverse hyperbolic function as the DRL component was increased from 1 to 24 sec within the constant 30-sec FI interval. Interresponse time and post-reinforcement (post-S^R) “break” distributions taken at one experimental point (DRL = 24 sec) suggested that a more precise temporal discrimination was initiated by an S^R than by a response, since the relative frequency of a sequence of two reinforced responses appeared greater than that of a sequence of a non-reinforced response followed by a reinforced one. This latter finding was confirmed with new animals in a follow-up experiment employing a conventional 24-sec DRL schedule.     

Collateral responding during differential reinforcement of low rates

Two pigeons were trained to peck either of two response keys for food, under two different variable-interval schedules. When responding stabilized, the schedule on the left key (reinforcement-key) was changed to a differential-reinforcement-of-low-rates schedule, and responses on the right key (extinction-key) were no longer reinforced. The mean interresponse time of responses on the reinforcement-key approximated the temporal requirement of the reinforcement schedule on that key. Collateral responding on the extinction-key was maintained by one of the birds. A “run” of these collateral responses was defined as a sequence of responses on the extinction-key occurring between two responses on the reinforcement-key. For this one bird, collateral behavior, measured by mean time per run and mean number of responses per run, was an increasing function of the temporal requirements of the reinforcement schedule on the reinforcement key, and it was strongly positively correlated with the mean interresponse time of responses on the reinforcement-key. However, from an analysis of the results, the collateral behavior did not appear to have mediated the temporal spacing of responses on the reinforcement-key.     

Changes in functional response units with briefly delayed reinforcement

In two experiments, key-peck responding of pigeons was compared under variable-interval schedules that arranged immediate reinforcement and ones that arranged unsignaled delays of reinforcement. Responses during the nominal unsignaled delay periods had no effect on the reinforcer presentations. In Experiment 1, the unsignaled delays were studied using variable-interval schedules as baselines. Relative to the immediate reinforcement condition, 0.5-s unsignaled delays decreased the duration of the reinforced interresponse times and increased the overall frequency of short (<0.5-s) interresponse times. Longer, 5.0-s unsignaled delays increased the duration of the reinforced interresponse times and decreased the overall frequency of the short interresponse times. In Experiment 2, similar effects to those of Experiment 1 were obtained when the 0.5-s unsignaled delays were imposed upon a baseline schedule that explicitly arranged reinforcement of short interresponse times and therefore already generated a large number of short interresponse times. The results support earlier suggestions that the unsignaled 0.5-s delays change the functional response unit from a single key peck to a multiple key-peck unit. These findings are discussed in terms of the mechanisms by which contingencies control response structure in the absence of specific structural requirements.     

Choice between response rates

Three pigeons were required to peck a single key at a higher and a lower rate, corresponding to two classes of shorter and longer concurrently reinforced interresponse times. Food reinforcers arranged by a single variable-interval schedule were randomly allocated to the two reinforced interresponse times. The absolute durations of reinforced interresponse times were varied while the total reinforcements per hour was held constant and the relative duration, i.e., the relative reciprocal, of the shorter reinforcer class was held constant at 0.70. Preference for the higher rate of responding, as measured by the relative frequency of responses terminating interresponse times in the shorter reinforced class, depended on the absolute reinforced response rates. Preference for the higher reinforced rate increased from a level of near-indifference (0.50) at high reinforced response rates, through the matching level (0.70) at intermediate reinforced response rates, to a virtually exclusive preference (>0.90) at low reinforced response rates. These results resemble corresponding preference functions obtained with two-key concurrent-chains schedules and thereby provide another sense in which it may be said that interresponse-time distributions from interval schedules estimate preference functions for the component response rates corresponding to different classes of reinforced interresponse times.     

Selective attention: the effects of combining stimuli which control incompatible behavior

Four rhesus monkeys learned both a color and tilt discrimination. The stimuli were combined to produce incompatible behavior. The behavior controlled by one set of stimuli was reinforced until “errors” virtually disappeared. The stimuli were tested separately again. Sixteen replications of the entire procedure indicated that the stimuli producing “errors” were ignored.     

Unbiased and unnoticed verbal conditioning: the double agent robot procedure

Subjects who were told they were “experimenters” attempted to reinforce fluent speech in a supposed subject with whom they spoke via intercom. The supposed subject was to say nouns, one at a time, on request by the “experimenter”, who reinforced fluent pronunciation with points. Actually, the “experimenter” was talking to a multi-track tape recording, one track of which contained fluently spoken nouns, the other track containing disfluently spoken nouns. If the “experimenter's” request for the next noun was in a specified form a word from the fluent track was played to him as reinforcement; requests in any other form produced the word from the disfluent track. Repeated conditioning of specific forms of requests was accomplished with two subject-“experimenters,” who were unable to describe changes in their own behavior, or the contingencies applied. This technique improved upon an earlier method that had yielded similar results, but was less thoroughly controlled against possible human bias.     

Recognition by the pigeon of stimuli varying in two dimensions

Pigeons served in four experiments, each of which involved about 44,000 discrete 1.2-sec trials under steady-state conditions. The first experiment scaled a short segment of the visual wavelength continuum; this dimension was then combined in a conditional discrimination with each of three others; time after reinforcement, tone frequency, and line tilt. In the two-stimulus experiments, the birds' responses were reinforced in the presence of only one stimulus combination: “582 nm” together with “2 min after reinforcement”, “3990 Hz”, or “vertical line”. Many other stimulus combinations also appeared equally often and went without reinforcement. The wavelength stimuli conformed to an equal-interval scale, and per cent response was generally linear with wavelength, when scaled on cumulative normal coordinates. The components of the compound stimulus were found to interact in a multiplicative fashion; when one component differed greatly from its reinforcement value, changes in the other component had relatively little effect. For the “time”-“wavelength” compound, this interaction appeared to be modified by the effects of set or attention. Certain response latency data are reported, and other combination rules are discussed.     

Spaced responding and choice: a preliminary analysis

Pigeons were exposed to reinforcement both for short (2 < IRT < 3 sec) and long (10 < IRT < 11 sec) interresponse times. They developed bimodal interresponse-time distributions, which were decomposable into two independent component distributions under the control of the short and long contingencies respectively. The birds' allocation of responses between these two distributions was determined by a simple power-law relationship between reinforcement ratios, and response ratios derived from the component distributions. Comparison between this situation and concurrent choice situations raises the possibility that the power-law relation between ratios may be a more general law of choice than the matching of relative frequencies (probabilities).     

Pigeons'' spatial memory: II. Acquisition of delayed matching of key location and transfer to new locations

Five hungry pigeons first received delayed matching of key location training. Trials began with a “ready” stimulus (brief operation of the grain feeder). Then one (randomly chosen) of a set of four keys from a three-by-three matrix was lit briefly as the sample. After a short delay (retention interval), the sample key was lit again along with one of the other eight keys. A peck at the key that had served as the sample produced grain reinforcement, whereas a peck to the other key produced only the intertrial interval. After delayed matching of key location was learned, the remaining five key locations were introduced as samples. Four of the five birds performed at considerably above-chance levels on the novel sample trials during the first as well as subsequent sessions. These results suggest that pigeons sometimes learn the single rule—“choose the location that matches the sample.” The relevance of these results to the issue of whether pigeons learn a generalized matching rule (i.e., a concept of “sameness”) is discussed.     

Concurrent schedules of interresponse time reinforcement: probability of reinforcement and the lower bounds of the reinforced interresponse time intervals

Data were obtained with rats on the effects of interresponse time contingent reinforcement of the lever press response using schedules in which interresponse times falling within either of two temporal intervals could be reinforced. Some of the findings were (a) the mode of the interresponse time distribution generally occurred near the first lower bound when the maximum reinforcement rate for the two lower bounds was equal; this also frequently occurred even when the reinforcement rate was less for the first lower bound; (b) as is the case with schedules using a single interval of reinforced interresponse times the values of the lower bounds partially determined the location and spread of the distributions; but the particular pair of values used did not seem to influence the effects of the probabilities of reinforcement; (c) although the modal interresponse time was usually at the lower bound of one of the two intervals of reinforced interresponse times, no simple relation existed between either the probability or rate of reinforcement of interresponse times in these two intervals and the location of this mode.     

Choice as time allocation

When pigeons' standing on one or the other side of a chamber was reinforced on two concurrent variable-interval schedules, the ratio of time spent on the left to time spent on the right was directly proportional to the ratio of reinforcements produced by standing on the left to reinforcements produced by standing on the right. The constant of proportionality was less than unity for all pigeons, indicating a bias toward the right side of the chamber. The biased matching relation obtained here is comparable to the matching relation obtained with concurrent reinforcement of key pecks. The present results, together with related research, suggest that the ratio of time spent in two activities equals the ratio of the “values” of the activities. The value of an activity is the product of several parameters, such as rate and amount of reinforcement, contingent on that activity.     

Response-rate differences in variable-interval and variable-ratio schedules: An old problem revisited

In Experiment 1, a variable-ratio 10 schedule became, successively, a variable-interval schedule with only the minimum interreinforcement intervals yoked to the variable ratio, or a variable-interval schedule with both interreinforcement intervals and reinforced interresponse times yoked to the variable ratio. Response rates in the variable-interval schedule with both interreinforcement interval and reinforced interresponse time yoking fell between the higher rates maintained by the variable-ratio schedule and the lower rates maintained by the variable-interval schedule with only interreinforcement interval yoking. In Experiment 2, a tandem variable-interval 15-s variable-ratio 5 schedule became a yoked tandem variable-ratio 5 variable-interval x-s schedule, and a tandem variable-interval 30-s variable-ratio 10 schedule became a yoked tandem variable-ratio 10 variable-interval x-s schedule. In the yoked tandem schedules, the minimum interreinforcement intervals in the variable-interval components were those that equated overall interreinforcement times in the two phases. Response rates did not decline in the yoked schedules even when the reinforced interresponse times became longer. Experiment 1 suggests that both reinforced interresponse times and response rate–reinforcement rate correlations determine response-rate differences in variable-ratio 10 and yoked variable-interval schedules in rats. Experiment 2 suggests a minimal role for the reinforced interresponse time in determining response rates on tandem variable-interval 30-s variable-ratio 10 and yoked tandem variable-ratio 10 variable-interval x-s schedules in rats.     

Programming stimuli in matching to sample

In these investigations, a “teaching machine” was used to train pre-school and first-grade children in a series of progressively difficult discrimination tasks, leading up to matching to sample. Such training was much more efficient than training in the final discrimination alone. The errors the subjects made were found to be a functon both of the differences between consecutive discriminations (the “size of the steps” in the program) and the length of training on each discrimination. Theoretical and practical implications of these findings are discussed.     

“Lying” in the pigeon

Two pigeons were taught to use symbols to communicate information about hidden colors to each other. When reporting red was more generously reinforced than reporting yellow or green, both birds passed through a period in which they “lied” by reporting another color as red.     

Bias in self-evaluation: Signal probability effects

Two experiments examined apparent signal probability effects in simple verbal self-reports. After each trial of a delayed matching-to-sample task, young adults pressed either a “yes” or a “no” button to answer a computer-presented query about whether the most recent choice met a point contingency requiring both speed and accuracy. A successful matching-to-sample choice served as the “signal” in a signal-detection analysis of self-reports. Difficulty of matching to sample, and thus signal probability, was manipulated via the number of nonmatching sample and comparison stimuli. In Experiment 1, subjects exhibited a bias (log b) for reporting matching-to-sample success when success was frequent, and no bias or a bias for reporting failure when success was infrequent. Contingencies involving equal conditional probabilities of point consequences for “I succeeded” and “I failed” reports had no systematic effect on this pattern. Experiment 2 found signal probability effects to be evident regardless of whether referent-response difficulty was manipulated in different conditions or within sessions. These findings indicate that apparent signal probability effects in self-report bias that were observed in previous studies probably were not an artifact of contingencies intended to improve self-report accuracy or of the means of manipulating signal probability. The findings support an analogy between simple self-reports and psychophysical judgments and bolster the conclusion of Critchfield (1993) that signal probability effects can influence simple self-reports much as they do reports about external stimuli in psychophysical experiments.     

The copyist model of response emission

The variety of different performances maintained by schedules of reinforcement complicates comprehensive model creation. The present account assumes the simpler goal of modeling the performances of only variable reinforcement schedules because they tend to maintain steady response rates over time. The model presented assumes that rate is determined by the mean of interresponse times (time between two responses) between successive reinforcers, averaged so that their contribution to that mean diminishes exponentially with distance from reinforcement. To respond, the model randomly selects an interresponse time from the last 300 of these mean interresponse times, the selection likelihood arranged so that the proportion of session time spent emitting each of these 300 interresponse times is the same. This interresponse time defines the mean of an exponential distribution from which one is randomly chosen for emission. The response rates obtained approximated those found on several variable schedules. Furthermore, the model reproduced three effects: (1) the variable ratio maintaining higher response rates than does the variable interval; (2) the finding for variable schedules that when the reinforcement rate varies from low to high, the response rate function has an ascending and then descending limb; and (3) matching on concurrent schedules. Because these results are due to an algorithm that reproduces reinforced interresponse times, responding to single and concurrent schedules is viewed as merely copying what was reinforced before.     

A molecular analysis of multiple schedule interactions: negative contrast

The present experiments investigated the relationship between changes in the relative reinforced interresponse-time distributions and the occurrence of positive and negative contrast in multiple variable-interval—variable-interval and multiple variable-interval—extinction schedules of reinforcement. Experiment I demonstrated that changes in the interresponse-time distributions were consistently correlated with response-rate changes referred to as positive and negative contrast. Corresponding changes in the reinforced interresponse-time distributions suggested that negative contrast resulted as an inductive effect of selectively reinforcing long interresponse times in the altered component at the moment the baseline schedule was reintroduced. Experiment II demonstrated that the magnitude of the negative-contrast effect could be significantly decreased if the altered component schedule was modified in order to prevent the reinforcement of these interresponse times during the first few sessions of baseline recovery. The results supported a proposal that interresponse time—reinforcer relations may act as amplifiers or attenuators of negative contrast.     

Operant and nonoperant vocal responding in the mynah: Complex schedule control and deprivation-induced responding

Several recent studies have been concerned with operant responses that are also affected by nonoperant factors, (e.g., biological constraints, innate behavior patterns, respondent processes). The major reason for studying mynah vocal responding concerned the special relation of avian vocalizations to nonoperant emotional and reflexive systems. The research strategy was to evaluate operant and nonoperant control by comparing the schedule control obtained with the vocal response to that characteristic of the motor responses of other animals. We selected single, multiple, and chain schedules that ordinarily produce disparate response rates at predictable times. In multiple schedules with one component where vocal responding (“Awk”) was reinforced with food (fixed-ratio or fixed-interval schedule) and one where the absence of vocal responding was reinforced (differential reinforcement of other behavior), response rates never exceeded 15 responses per minute, but clear schedule differences developed in response rate and pause time. Nonoperant vocal responding was evident when responding endured across 50 extinction sessions at 25% to 40% of the rate during reinforcement. The “enduring extinction responding” was largely deprivation induced, because the operant-level of naive mynahs under food deprivation was comparable in magnitude, but without deprivation the operant level was much lower. Food deprivation can induce vocal responding, but the relatively precise schedule control indicated that operant contingencies predominate when they are introduced.