Randomized Allocation of Treatments in Sequential Experiments

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1981 · Volume 43 · Issue 3

DOI: 10.1111/j.2517-6161.1981.tb01672.x

Abstract

Since the idea of sequential allocation was first studied, in a version of what is now called the multi-armed bandit problem, the results of many investigations have shown that, even when an optimal allocation rule can be found, its form depends on the parameters of the model and no single rule has emerged that is widely acceptable in practice. On the other hand, it can be shown that conventional methods, using equal allocations of the treatments under comparison, involve many unnecessary applications of inferior treatments even if the final choice of the “best” treatment relies on a sequential test. The evidence for this claim is based on an investigation of randomized allocation rules, where the choice of the next treatment is randomized in such a way that some preference is given to the “favourite” at any stage, but other treatments are not permanently excluded.

Keywords

bandit processes, randomized allocation indices, markov decision processes, bayes procedures, minimax policies, sequential medical trials

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