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To behave adaptively in environments that are noisy and nonstationary, humans and other animals must monitor feedback from their environment and adjust their predictions and actions accordingly. An understudied approach for modeling these adaptive processes comes from the engineering field of control theory, which provides general principles for regulating dynamical systems, often without requiring a generative model. The proportional-integral-derivative (PID) controller is one of the most popular models of industrial process control. The proportional term is analogous to the "delta rule" in psychology, adjusting estimates in proportion to each error in prediction. The integral and derivative terms augment this update to simultaneously improve accuracy and stability. Here, we tested whether the PID algorithm can describe how people sequentially adjust their predictions in response to new information. Across three experiments, we found that the PID controller was an effective model of participants' decisions in noisy, changing environments. In Experiment 1, we reanalyzed a change-point detection experiment and showed that participants' behavior incorporated elements of PID updating. In Experiments 2-3, we developed a task with gradual transitions that we optimized to detect PID-like adjustments. In both experiments, the PID model offered better descriptions of behavioral adjustments than both the classical delta-rule model and its more sophisticated variant, the Kalman filter. We further examined how participants weighted different PID terms in response to salient environmental events, finding that these control terms were modulated by reward, surprise, and outcome entropy. These experiments provide preliminary evidence that adaptive learning in dynamic environments resembles PID control.

A Control Theoretic Model of Adaptive Learning in Dynamic Environments