Upper-Confidence-Bound Algorithms for Active Learning in Multi-Armed Bandits
This work addresses adaptive sampling in multi-armed bandits for active learning, offering incremental improvements in allocation strategies for unknown distributions.
The paper tackles the problem of estimating the means of multiple distributions with a finite sample budget by developing adaptive sampling strategies based on upper-confidence bounds on variance, showing that performance depends on both variances and distribution shapes.
In this paper, we study the problem of estimating uniformly well the mean values of several distributions given a finite budget of samples. If the variance of the distributions were known, one could design an optimal sampling strategy by collecting a number of independent samples per distribution that is proportional to their variance. However, in the more realistic case where the distributions are not known in advance, one needs to design adaptive sampling strategies in order to select which distribution to sample from according to the previously observed samples. We describe two strategies based on pulling the distributions a number of times that is proportional to a high-probability upper-confidence-bound on their variance (built from previous observed samples) and report a finite-sample performance analysis on the excess estimation error compared to the optimal allocation. We show that the performance of these allocation strategies depends not only on the variances but also on the full shape of the distributions.