  We consider a decision maker who must choose an action in order to maximize a
reward function that depends also on an unknown parameter {\Theta}. The
decision maker can delay taking the action in order to experiment and gather
additional information on {\Theta}. We model the decision maker's problem using
a Bayesian sequential experimentation framework and use dynamic programming and
diffusion-asymptotic analysis to solve it. For that, we scale our problem in a
way that both the average number of experiments that is conducted per unit of
time is large and the informativeness of each individual experiment is low.
Under such regime, we derive a diffusion approximation for the sequential
experimentation problem, which provides a number of important insights about
the nature of the problem and its solution. Our solution method also shows that
the complexity of the problem grows only quadratically with the cardinality of
the set of actions from which the decision maker can choose. We illustrate our
methodology and results using a concrete application in the context of
assortment selection and new product introduction. Specifically, we study the
problem of a seller who wants to select an optimal assortment of products to
launch into the marketplace and is uncertain about consumers' preferences.
Motivated by emerging practices in e-commerce, we assume that the seller is
able to use a crowdvoting system to learn these preferences before a final
assortment decision is made. In this context, we undertake an extensive
numerical analysis to assess the value of learning and demonstrate the
effectiveness and robustness of the heuristics derived from the diffusion
approximation.
