Feedback functions, optimization, and the relation of response rate to reinforcer rate.
Behavior locks to the peak of the feedback curve, so schedule shape is your main lever, not reinforcer count.
01Research in Context
What this study did
Lecavalier et al. (2006) built special schedules for rats. The lever gave food only when the rat pressed at the sweet spot of an upside-down U curve.
Too fast or too slow earned nothing. The team watched where each rat settled its pace.
What they found
The rats landed near the top of the U. They did not chase the highest food rate.
Schedule shape, not food count, set the final speed.
How this fits with other research
Hawkes et al. (1974) saw the same idea earlier. Rats shifted presses to grab the most brain stimulation. That paper planted the seed: animals maximize, not match.
Kuroda et al. (2018) added a twist. They showed that the response-food correlation alone can drive rate. The 2006 vertex rule still holds, but now we know the correlation is one cue the rat uses to find it.
Byrne et al. (2019) stretched the rule further. Rats tuned press duration, not just speed, to earn food. Optimization applies to how long a response lasts, not just how often it happens.
Why it matters
When you write a schedule, picture the feedback function your client faces. A dense DRL can still cut behavior if the peak sits at a low rate. A thin VR may spike rate if the vertex is high. Sketch the curve first, then pick the numbers.
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02At a glance
03Original abstract
The present experiment arranged a series of inverted U-shaped feedback functions relating reinforcer rate to response rate to test whether responding was consistent with an optimization account or with a one-to-one relation of response rate to reinforcer rate such as linear system theory's rate equation or Herrnstein's hyperbola. Reinforcer rate was arranged according to a quadratic equation with a maximum at a unique response rate. The experiment consisted of two phases, during which 6 Long Evans rats lever pressed for food. In the first phase of the experiment, the rats responded on six fixed-interval-plus-quadratic-feedback schedules, and in the second phase the rats responded on three variable-interval-plus-quadratic-feedback schedules. Responding in both phases was inconsistent with a one-to-one relation of response rate to reinforcer rate. Instead, different response rates were obtained at equivalent reinforcer rates. Responding did vary directly with the vertex of the feedback function in both phases, a finding consistent with optimization of reinforcer rate. The present results suggest that the feedback function relating reinforcer rate to response rate imposed by a reinforcement schedule can be an important determinant of behavior. Furthermore, the present experiment illustrates the benefit of arranging feedback functions to investigate assumptions about the variables that control schedule performance.
Journal of the experimental analysis of behavior, 2006 · doi:10.1901/jeab.2006.13-05