When fitting the learning data of an individual to algorithm-like learning models, the observations are so dependent and non-stationary that one may wonder what the classical Maximum Likelihood Estimator (MLE) could do, even if it is the usual tool applied to experimental cognition. Our objective in this work is to show that the estimation of the learning rate cannot be efficient if the learning rate is constant in the classical Exp3 (Exponential weights for Exploration and Exploitation) algorithm. Secondly, we show that if the learning rate decreases polynomially with the sample size, then the prediction error and in some cases the estimation error of the MLE satisfy bounds in probability that decrease at a polynomial rate.

翻译：在将个体的学习数据拟合至类算法学习模型时，观测数据呈现高度依赖性和非平稳性，以至于人们可能会质疑经典最大似然估计（MLE）在此类场景下的表现——即便它是实验认知研究中常用的工具。本文旨在证明：当经典Exp3（探索与利用的指数加权）算法中的学习率为常数时，学习率的估计无法实现有效收敛。其次，我们进一步证明：若学习率随样本量呈多项式衰减，则MLE的预测误差（某些情况下包括估计误差）的概率界将以多项式速率递减。