Learning the distribution with largest mean: two bandit frameworks
This is an incremental review paper for researchers in machine learning and bandit theory, summarizing existing frameworks without introducing new methods.
The paper reviews two sequential learning tasks in multi-armed bandit models—regret minimization and best arm identification—aimed at finding the distribution with the highest mean, and presents asymptotically optimal algorithms for each, comparing their sampling rules and complexity terms.
Over the past few years, the multi-armed bandit model has become increasingly popular in the machine learning community, partly because of applications including online content optimization. This paper reviews two different sequential learning tasks that have been considered in the bandit literature ; they can be formulated as (sequentially) learning which distribution has the highest mean among a set of distributions, with some constraints on the learning process. For both of them (regret minimization and best arm identification) we present recent, asymptotically optimal algorithms. We compare the behaviors of the sampling rule of each algorithm as well as the complexity terms associated to each problem.