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In this paper we consider the two-armed bandit problem, which often naturallyappears per se or as a subproblem in some multi-armed generalizations, andserves as a starting point for introducing additional problem features. Theconsideration of binary responses is motivated by its widespread applicabilityand by being one of the most studied settings. We focus on the undiscountedfinite-horizon objective, which is the most relevant in many applications. Wemake an attempt to unify the terminology as this is different acrossdisciplines that have considered this problem, and present a unified model castin the Markov decision process framework, with subject responses modelled usingthe Bernoulli distribution, and the corresponding Beta distribution forBayesian updating. We give an extensive account of the history and state of theart of approaches from several disciplines, including design of experiments,Bayesian decision theory, naive designs, reinforcement learning, biostatistics,and combination designs. We evaluate these designs, together with a few newlyproposed, accurately computationally (using a newly written package in Juliaprogramming language by the author) in order to compare their performance. Weshow that conclusions are different for moderate horizons (typical in practice)than for small horizons (typical in academic literature reporting computationalresults). We further list and clarify a number of myths about this problem,e.g., we show that, computationally, much larger problems can be designed toBayes-optimality than what is commonly believed.

The Finite-Horizon Two-Armed Bandit Problem with Binary Responses: A Multidisciplinary Survey of the History, State of the Art, and Myths