A mathematical model is presented descriptive of instrumental learning, i.e. operant conditioning. An agent learns to commit a certain number of acts per time unit, distributed as a non-stationary Poisson process. The derivative of the agent's expected utility per time unit, where utility is expected benefit minus expected cost, is interpreted as his drive to reach a local maximum of his expected utility. This drive multiplied with his act intensity are proportional to the change of the agent's act intensity per time unit, which is an ordinary first order differential equation for instrumental learning.
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