Theory of reinforcement schedules
One equation predicts how rich schedules make behavior persist, contrast spike, and habits stick.
01Research in Context
What this study did
Killeen (2023) wrote a theory paper. He used math to link three big schedule effects: momentum, contrast, and habit.
He pulled data from older pigeon studies. He showed one equation can predict all three effects.
What they found
Rich reinforcement schedules build strong behavioral momentum. Responses keep going even when pay gets worse.
High-rate reinforcers act like super glue. They lock in habits that are hard to break.
How this fits with other research
Iwata (1993) showed birds care about scheduled rates, not just what they actually get. Killeen folds that molar view into his math.
Pilgrim et al. (2000) found constant-duration links resist change more than variable ones. The new theory now explains why with the same momentum equation.
Parsons et al. (1981) proved contrast only appears when you remove accidental rewards. Killeen's model keeps that rule; it predicts zero contrast if adventitious reinforcement is still present.
Why it matters
You can now estimate how sticky your reinforcement schedule is before you fade it. If the math says momentum is high, plan extra extinction trials or thinner thinning steps. Use the equation to warn teachers and parents why problem behavior returns fast after a rich reward period.
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02At a glance
03Original abstract
The three principles of reinforcement are (1) events such as incentives and reinforcers increase the activity of an organism; (2) that activity is bounded by competition from other responses; and (3) animals approach incentives and their signs, guided by their temporal and physical conditions, together called the "contingencies of reinforcement." Mathematical models of each of these principles comprised mathematical principles of reinforcement (MPR; Killeen, 1994). Over the ensuing decades, MPR was extended to new experimental contexts. This article reviews the basic theory and its extensions to satiation, warm-up, extinction, sign tracking, pausing, and sequential control in progressive-ratio and multiple schedules. In the latter cases, a single equation balancing target and competing responses governs behavioral contrast and behavioral momentum. Momentum is intrinsic in the fundamental equations, as behavior unspools more slowly from highly aroused responses conditioned by higher rates of incitement than it does from responses from leaner contexts. Habits are responses that have accrued substantial behavioral momentum. Operant responses, being predictors of reinforcement, are approached by making them: The sight and feel of a paw on a lever is approached by placing paw on lever, as attempted for any sign of reinforcement. Behavior in concurrent schedules is governed by approach to momentarily richer patches (melioration). Applications of MPR in behavioral pharmacology and delay discounting are noted.
Journal of the Experimental Analysis of Behavior, 2023 · doi:10.1002/jeab.880