On the convergence of the MLE as an estimator of the learning rate in the Exp3 algorithm
This addresses a methodological issue for researchers in experimental cognition and machine learning, providing theoretical insights into estimator efficiency in non-stationary, dependent data settings, but it is incremental as it builds on existing Exp3 and MLE frameworks.
The paper tackles the problem of estimating the learning rate in the Exp3 algorithm using the Maximum Likelihood Estimator (MLE), showing that estimation is inefficient with a constant learning rate but achieves polynomial-rate bounds for prediction and estimation errors when the learning rate decreases polynomially with sample size.
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.