A Selecting-the-Best Method for Budgeted Model Selection

The paper focuses on budgeted model selection, that is the selection between a set of alternative models when the ratio between the number of model assessments and the number of alternatives, though bigger than one, is low. We propose an approach based on the notion of probability of correct selection, a notion borrowed from the domain of Monte Carlo stochastic approximation. The idea is to estimate from data the probability that a greedy selection returns the best alternative and to define a sampling rule which maximises such quantity. Analytical results in the case of two alternatives are extended to a larger number of alternatives by using the Clark’s approximation of the maximum of a set of random variables. Preliminary results on synthetic and real model selection tasks show that the technique is competititive with state-ofthe-art algorithms, like the bandit UCB.