Uncertain Search with Knowledge Transfer

We consider a sequential search over a group of similar alternatives. The individual value of an alternative contains two components, an observable utility and an idiosyncratic value. Once an alternative is searched, the utility can be fully revealed, but the idiosyncratic value is unobservable and needs to be learned gradually by sampling. The utilities share an unknown population distribution, which captures the similarity across the alternatives and allows for knowledge transfer within the group. The goal is to select an alternative with the highest individual value while accounting for the sampling and search costs. A novel feature of this problem is the combination of the individual and population levels of learning. We formulate the problem as a Bayesian dynamic program and characterize the optimal policy by a threshold structure. We show that it depends on the difference between the mean estimates of the current alternative and the population. It is optimal to continue sampling if the difference is between a threshold pair; otherwise, accept the current alternative if it exceeds the upper threshold and switch to a new one if it is below the lower threshold. Other structural properties are also derived to shed light on the effects of the two levels of learning. Moreover, we extend our model and structural results to practical variants where (i) the sample precision is unknown, (ii) the population distribution is high-dimensional, and (iii) the goal is to select multiple alternatives