Optimal Learning From Multiple Information Sources (joint with Xiaosheng Mu and Vasilis Syrgkanis)
Last updated: May 15, 2017
Abstract. Consider a decision-maker who sequentially acquires Gaussian signals from distinct and possibly complementary sources for a future decision. Which sources should he choose to observe in each period? In environments that we characterize, it turns out that the dynamically optimal path of signal acquisitions: (1) exactly coincides at every period with the myopic path of signal acquisitions, and (2) achieves "total optimality," so that at every late period, the decision-maker will not want to revise his previous signal acquisitions even if given this opportunity. We show that generically, these properties hold at all sufficiently late times, so that the dynamically optimal path and myopic path are eventually equivalent. Moreover, these results hold independently of the decision problem and the timing of the decision, so that the optimal rule is robust to these specifications. These results stand in contrast to a large body of dynamic learning and optimal experimentation problems in which the dynamically optimal solution can only be approximated or implicitly characterized.