An adaptive step-size algorithm [Kushner and Yin,Stochastic Approximation and Recursive Algorithms and Applications, 2nd ed., New York: Springer-Verlag (2003)] is used to model time-varying learning, and its performance is illustrated in the environment of Marcet and Nicolini [American Economic Review93 (2003), 1476–1498]. The resulting model gives qualitatively similar results to those of Marcet and Nicolini, and performs quantitatively somewhat better, based on the criterion of mean squared error. The model generates increasing gain during hyperinflations and decreasing gain after hyperinflations end, which matches findings in the data. An agent using this model behaves cautiously when faced with sudden changes in policy, and is able to recognize a regime change after acquiring sufficient information.
In-flight range optimization of multicopters using multivariable extremum seeking with adaptive step size