Hill-climbing by pigeons

Pigeons were exposed to two types of concurrent operant-reinforcement schedules in order to determine what choice rules determine behavior on these schedules. In the first set of experiments, concurrent variable-interval, variable-interval schedules, key-peck responses to either of two alternative schedules produced food reinforcement after a random time interval. The frequency of food-reinforcement availability for the two schedules was varied over different ranges for different birds. In the second series of experiments, concurrent variable-ratio, variable-interval schedules, key-peck responses to one schedule produced food reinforcement after a random time interval, whereas food reinforcement occurred for an alternative schedule only after a random number of responses. Results from both experiments showed that pigeons consistently follow a behavioral strategy in which the alternative schedule chosen at any time is the one which offers the highest momentary reinforcement probability (momentary maximizing). The quality of momentary maximizing was somewhat higher and more consistent when both alternative reinforcement schedules were time-based than when one schedule was time-based and the alternative response-count based. Previous attempts to provide evidence for the existence of momentary maximizing were shown to be based upon faulty assumptions about the behavior implied by momentary maximizing and resultant inappropriate measures of behavior.     

Reinforcement of least-frequent sequences of choices

When a pigeon's choices between two keys are probabilistically reinforced, as in discrete trial probability learning procedures and in concurrent variable-interval schedules, the bird tends to maximize, or to choose the alternative with the higher probability of reinforcement. In concurrent variable-interval schedules, steady-state matching, which is an approximate equality between the relative frequency of a response and the relative frequency of reinforcement of that response, has previously been obtained only as a consequence of maximizing. In the present experiment, maximizing was impossible. A choice of one of two keys was reinforced only if it formed, together with the three preceding choices, the sequence of four successive choices that had occurred least often. This sequence was determined by a Bernoulli-trials process with parameter p. Each of three pigeons matched when p was ½ or ¼. Therefore, steady-state matching by individual birds is not always a consequence of maximizing. Choice probability varied between successive reinforcements, and sequential statistics revealed dependencies which were adequately described by a Bernoulli-trials process with p depending on the time since the preceding reinforcement.     

More on concurrent interval-ratio schedules: a replication and review.

It has been suggested that the failure to maximize reinforcement on concurrent variable-interval, variable-ratio schedules may be misleading. Inasmuch as response costs are not directly measured, it is possible that subjects are optimally balancing the benefits of reinforcement against the costs of responding. To evaluate this hypothesis, pigeons were tested in a procedure in which interval and ratio schedules had equal response costs. On a concurrent variable time (VT), variable ratio-time (VRT) schedule, the VT schedule runs throughout the session and the VRT schedule is controlled by responses to a changeover key that switches from one schedule to the other. Reinforcement is presented independent of response. This schedule retains the essential features of concurrent VI VR, but eliminates differential response costs for the two alternatives. It therefore also eliminates at least one significant ambiguity about the reinforcement maximizing performance. Pigeons did not maximize rate of reinforcement on this procedure. Instead, their times spent on the alternative schedules matched the relative rates of reinforcement, even when schedule parameters were such that matching earned the lowest possible overall rate of reinforcement. It was further shown that the observed matching was not a procedural artifact arising from the constraints built into the schedule.     

Choice behavior in a discrete-trial concurrent VI-VR: A test of maximizing theories of matching

Rats were trained on a discrete-trial procedure in which one alternative (VR) was correlated with a constant probability of reinforcement while the other was correlated with a VI schedule which ran during the intertrial intervals and held the scheduled reinforcer until they were obtained by the next VI response. Relative reinforcement rate was varied in series of conditions in which the VR schedule was varied and in series in which the VI was varied. Choice behavior was described well by the generalized matching law, although moderate undermatching occurred for all subjects. Contrary to the predictions of molar maximizing (optimality) theories, there was no consistent bias in favor of the ratio alternative, and the sensitivity to reinforcement allocation was not systematically affected by whether the ratio or interval schedule was varied. The results were also contrary to momentary maximizing accounts, as there was no correspondence between the probability of a changeover to the VI behavior and the time since the last response to the VI alternative. Neither variety of maximizing theory appears to provide a general explanation of matching in concurrent schedules.     

Concurrent variable-interval variable-ratio schedules can provide only weak evidence for matching

Herrnstein and Heyman (1979) showed that when pigeons' pecking is reinforced on concurrent variable-interval variable-ratio schedules, (1) their behavior ratios match the ratio of the schedules' reinforcer frequencies, and (2) there is more responding on the variable interval. Since maximizing the reinforcement rate would require responding more on the variable ratio, these results were presented as establishing the primacy of matching over maximizing. In the present report, different ratios of behavior were simulated on a computer to see how they would affect reinforcement rates on these concurrent schedules. Over a wide range of experimenter-specified choice ratios, matching obtained — a result suggesting that changes in choice allocation produced changes in reinforcer frequencies that correspond to the matching outcome. Matching also occurred at arbitrarily selected choice ratios when reinforcement rates were algebraically determined by each schedule's reinforcement-feedback function. Additionally, three birds were exposed to concurrent variable-interval variable-ratio schedules contingent on key pecking in which hopper durations were varied in some conditions to produce experimenter-specified choice ratios. Matching generally obtained between choice ratios and reinforcer-frequency ratios at these different choice ratios. By suggesting that reinforcer frequencies track choice on this procedure, instead of vice versa, this outcome questions whether matching-as-outcome was due to matching-as-process in the Herrnstein and Heyman study.     

Interresponse-time sensitivity during discrete-trial and free-operant concurrent variable-interval schedules

Two experiments investigated the sensitivity of pigeons' choice to elapsed time since the last response (i.e., to inter-response time [IRT]) during concurrent variable-interval variable-interval schedules. Experiment 1 used a two-key discrete-trial procedure with variable intertrial intervals. Experiment 2 employed a three-key free-operant procedure. In both experiments choice was found to be a function of the active-schedule IRT, defined as the time since the most recent response. Monte Carlo simulations show how this finding permits the joining of several seemingly incompatible data sets held to both support and contradict a kind of choice strategy, termed momentary maximizing, which attempts to maximize momentary reinforcement probabilities. The studies suggest that only two variables are needed to describe the static molecular structure of concurrent variable-interval choice: active-schedule IRTs and "response states" consisting of the last one or two schedule choices.     

A local model of concurrent performance

Concurrent procedures may be conceptualized as consisting of two pairs of schedules with only one pair operating at a time. One schedule of each pair arranges reinforcers for staying in the current alternative, and the other schedule arranges reinforcers for switching to the other alternative. These pairs alternate operation as the animal switches between choices. This analysis of the contingencies suggests that variables operating within an alternative produce behavior that conforms to the generalized matching law. Rats were exposed to one pair of stay and switch schedules in each condition, and the probabilities of reinforcement varied across conditions. Both run length and visit duration were power functions of the ratio of the probabilities of reinforcement for staying and switching. The local model, a model of performance on concurrent procedures, was derived from this power function. Performance on concurrent schedules was synthesized from the performances on the separate pairs. Both the generalized matching law and the local model fitted the synthesized concurrent performances. These results are consistent with the view that the contingencies in the alternative, the probability of stay and switch reinforcement, are responsible for performance consistent with the generalized matching law. These results are compatible with momentary maximizing and molar maximizing accounts of concurrent performance. Models of concurrent performance that posit comparisons among the alternatives are not easily applied to these results.     

Momentary maximizing in concurrent schedules with a minimum interchangeover interval

Eight pigeons were trained on concurrent variable-interval variable-interval schedules with a minimum interchangeover time programmed as a consequence of changeovers. In Experiment 1 the reinforcement schedules remained constant while the minimum interchangeover time varied from 0 to 200 s. Relative response rates and relative time deviated from relative reinforcement rates toward indifference with long minimum interchangeover times. In Experiment 2 different reinforcement ratios were scheduled in successive experimental conditions with the minimum interchangeover time constant at 0, 2, 10, or 120 s. The exponent of the generalized matching equation was close to 1.0 when the minimum interchangeover time was 0 s (the typical procedure for concurrent schedules without a changeover delay) and decreased as that duration was increased. The data support the momentary maximizing theory and contradict molar maximizing theories and the melioration theory.     

Maximizing and matching on concurrent ratio schedules

Pigeons on concurrent variable-ratio variable-ratio schedules usually, though not always, maximize reinforcements per response. When the ratios are equal, maximization implies no particular distribution of responses to the two alternatives. When the ratios are unequal, maximization calls for exclusive preference for the smaller ratio. Responding conformed to these requirements for maximizing, which are further shown to be consistent with the conception of reinforcement implicit in the matching law governing relative responding in concurrent interval schedules.     

Matching, maximizing, and hill-climbing

In simple situations, animals consistently choose the better of two alternatives. On concurrent variable-interval variable-interval and variable-interval variable-ratio schedules, they approximately match aggregate choice and reinforcement ratios. The matching law attempts to explain the latter result but does not address the former. Hill-climbing rules such as momentary maximizing can account for both. We show that momentary maximizing constrains molar choice to approximate matching; that molar choice covaries with pigeons' momentary-maximizing estimate; and that the “generalized matching law” follows from almost any hill-climbing rule.     

Drug discrimination under concurrent variable-ratio variable-ratio schedules

Pigeons were trained to discriminate 5 mg/kg pentobarbital from saline under concurrent variable-ratio (VR) VR schedules, in which responses on the pentobarbital-biased lever were reinforced under the VR schedule with the smaller response requirements when pentobarbital was given before the session, and responses on the saline-biased key were reinforced under the VR schedule with the larger response requirements. When saline was administered before the session, the reinforcement contingencies associated with the two response keys were reversed. When responding stabilized under concurrent VR 20 VR 30, concurrent VR 10 VR 40, or concurrent VR 5 VR 50 schedules, pigeons responded almost exclusively on the key on which fewer responses were required to produce the reinforcer. When other doses of pentobarbital and other drugs were substituted for the training dose, low doses of all drugs produced responding on the saline-biased key. Higher doses of pentobarbital and chlordiazepoxide produced responding only on the pentobarbital-biased key, whereas higher doses of ethanol and phencyclidine produced responding only on this key less often. d-Amphetamine produced responding primarily on the saline-biased key. When drugs generalized to pentobarbital, the shape of the generalization curve under concurrent VR VR schedules was more often graded than quantal in shape. Thus, drug discrimination can be established under concurrent VR VR schedules, but the shapes of drug-discrimination dose-response curves under concurrent VR VR schedules more closely resemble those seen under interval schedules than those seen under fixed-ratio schedules. Graded dose-response curves under concurrent VR VR schedules may relate to probability matching and difficulty in discriminating differences in reinforcement frequency.     

IS MATCHING COMPATIBLE WITH REINFORCEMENT MAXIMIZATION ON CONCURRENT VARIABLE INTERVAL,VARIABLE RATIO?1

Four pigeons on concurrent variable interval, variable ratio approximated the matching relationship with biases toward the variable interval when time spent responding was the measure of behavior and toward the variable ratio when frequency of pecking was the measure of behavior. The local rates of responding were consistently higher on the variable ratio, even when there was overall preference for the variable interval. Matching on concurrent variable interval, variable ratio was shown to be incompatible with maximization of total reinforcement, given the observed local rates of responding and rates of alternation between the schedules. Furthermore, it was shown that the subjects were losing reinforcements at a rate of about 60 per hour by matching rather than maximizing.     

Concurrent schedules: Maximization versus reinforcement of changeover behaviour

Pigeons responded on concurrent variable-interval 180-sec variable-interval 36-sec schedules during Conditions 1 and 3 of Experiment 1. Condition 2 arranged variable-interval 60-sec schedules for both response alternatives. The schedule assigned to the alternative that was associated with the variable-interval 36-sec schedule in Conditions 1 and 3 operated only when the subject responded on that alternative. The proportion of time spent responding on the alternative with the conventional variable-interval 60-sec schedule increased during Condition 2, but exclusive choice of that alternative did not develop. This result is inconsistent with maximization of the overall reinforcement rate and with maximization of the momentary probability of reinforcement (momentary maximizing). Increasing time proportions were also found in Experiment 2, which arranged similar conditions, except that reinforcement was provided on a variable-time basis. The time proportions were close to the momentary maximizing prediction in Experiment 2. The results of both experiments can be explained if it is assumed that time allocation is controlled by delayed reinforcement of changeovers between alternatives.     

Choice behavior on discrete trials: a demonstration of the occurrence of a response strategy

Three pairs of pigeons were trained to peck at two keys presented simultaneoulsy in discrete trials with intertrial intervals of 1, 22, or 120 sec. Left-key responses incremented the probability of reinforcement for the first right-key response and, conversely, right-key responses incremented the probability of reinforcement for the first left-key response. In terms of relative response rates, it was found that all birds' choices were described by a momentary maximizing strategy, but this fact was not reflected in the detailed sequential statistics for birds with the longer (22 or 120 sec) intertrial intervals. It was hypothesized that choice behavior, in general, may be accurately described by a momentary maximizing sequence, but that prior failures to demonstrate this were due to “errors” in executing the momentary maximizing sequence. These misappropriated responses, which are hypothesized to be randomly distributed among the responses defining the momentary maximizing sequence, caused successive choices to appear to be statistically independent when, in fact, they were not.     

Concurrent second-order schedules of reinforcement

Responses on one key (the main key) of a two-key chamber produced food according to a second-order variable-interval schedule with fixed-interval schedule components. A response on a second key (the changeover key) alternated colors on the main key and provided a second independent second-order variable-interval schedule with fixed-interval components. The fixed-interval component on one variable-interval schedule was held constant at 8 sec, while the fixed interval on the other variable-interval schedule was varied from 0 to 32 sec. Under some conditions, a brief stimulus terminated each fixed interval and generated fixed-interval patterns; in other conditions, the brief stimulus was omitted. Relative response rate and relative time deviated substantially from scheduled relative reinforcement rate and, to a lesser extent, from obtained relative reinforcement rate under both brief-stimulus and no-stimulus conditions. Matching was observed with equal components on both schedules; with unequal components, increasingly greater proportions of time and responses than the matching relation would predict were spent on the variable-interval schedule containing the shorter component. Preference for the shorter fixed interval was typically more extreme under brief-stimulus than under no-stimulus schedules. The results limit the extension of the matching relation typically observed under simple concurrent variable-interval schedules to concurrent second-order variable-interval schedules.     

A comparison of the key-peck and treadle-press operants in the pigeon: differential-reinforcement-of-low-rate schedule of reinforcement

Key pecking and treadle pressing in pigeons were compared under concurrent (key-treadle) and single-operant differential-reinforcement-of-low-rate schedules of food reinforcement ranging from 5 to 60 sec (concurrent procedure) or 5 to 120 sec (single-operant procedure). Under both procedures, the two operants followed the same general law: decreasing response rate and reinforcement rate and increasing number of responses per reinforcement as a function of increasing schedule interval. High correlations were found between key pecking and treadle pressing for the measures of response rate, reinforcement rate, and responses per reinforcement. Regression equations allowed the prediction of treadle pressing from key pecking. More bursting occurred in responding to the key, and key pecking showed a more precise temporal discrimination than treadle pressing. A test for sequential dependencies between key and treadle responses showed significant dependencies not only under the concurrent procedure but also in data created artificially by merging key and treadle sequences from different pigeons under the concurrent procedure and from the same pigeon under the single-operant procedure. It seems likely that the sequential dependencies found were due to the independent action of the schedule on each operant and that behavioral dependencies did not occur with the concurrent training procedure. The key-peck operant does not appear to have any special qualities that preclude its use in discovering general laws of behavior, at least under the differential-reinforcement-of-low-rate schedule. The usefulness of the key peck in other situations requires direct experimental study.     

Concurrent choice: Effects of overall reinforcer rate and the temporal distribution of reinforcers

Six pigeons responded on a series of concurrent exponential variable-interval schedules, offering a within-subject comparison with previously published data from concurrent arithmetic variable-interval schedules. Both relative and overall reinforcer rates were varied between conditions. The generalized matching law described the data well, with undermatching much more frequent than strict matching. Time-allocation sensitivity consistently exceeded response-allocation sensitivity for both schedule types, and exponential-schedule sensitivity exceeded arithmetic-schedule sensitivity for both measures of choice. A further set of conditions using variable-interval schedules whose shortest interval was correlated with the mean interval, like arithmetic schedules, but that provided a constant conditional probability of reinforcement, like exponential schedules, produced sensitivities between those produced by conventional arithmetic and exponential schedules. Unlike previous arithmetic-schedule results, exponential sensitivity changed nonmonotonically with changes in overall reinforcer rate. The results clarify our knowledge of the effects of arithmetic and exponential schedules but confuse our understanding of the effects of overall reinforcer rate on concurrent choice.     

Interval reinforcement of choice behavior in discrete trials

Pigeons were trained to peck at red or green keys presented simultaneously in discrete trials. In one experiment, reinforcements were arranged by concurrent variable-interval schedules. The proportion of responses to green approximately matched the proportion of reinforcements produced by pecking green. Detailed analysis of responding revealed a systematic decrease in the probability of switching from green to red within sequences of trials after reinforcement. This trend corresponded to sequential changes in the relative frequency of reinforcement, and not to sequential changes in probability of reinforcement. In a second experiment, reinforcements were scheduled probabilistically every seventh trial. Even though there were no contingencies on pecking during the first six post-reinforcement trials, choices of green on the first response after reinforcement matched the proportion of reinforcements for pecking green. These results extend the generality of overall matching under concurrent reinforcement.     

Relative and absolute reinforcement frequency as determinants of choice in concurrent variable interval schedules

Rats were trained under concurrent schedules consisting of two equal variable interval component shedules providing sucrose solutions of different concentrations (0.6 M, 0.2 M; 50 μl in each case) as the reinforcers. The mean interreinforcement interval specified by the schedules was varied from 10 to 640 sec. Absolute response rate in each component was an increasing hyperbolic function of reinforcement frequency. Relative response rate and relative time allocation revealed a consistent preference for the more concentrated solution; neither measure of preference was systematically related to reinforcement frequency. The results are consistent with Baum and Rachlin's (1969) extension of the matching law, and with a derivation of the matching law from the hyperbolic relation between absolute response rate and reinforcement frequency in variable interval schedules (Herrnstein, 1970).