Rate-reliability tradeoff in two-dimensional visual search

Consider the problem of sequentially searching for a single target in a uniform image. Let the image be divided into M × M equal sized segments where M determines the resolution of the search. In each step, the player can visually inspect an allowable combination of the segments and the outcome of the inspection is noisy. The goal is to find the segment that contains the target quickly and accurately. In this paper, a fundamental trade-off between the rate and reliability of information acquisition is established. More specifically, it is shown that as the expected duration of search increases there is a fundamental tension between increasing the resolution of the search versus decreasing the error probability. The proof relies on a lower bound, obtained via a dynamic programming formulation, and an achievability scheme that maximizes the Extrinsic Jensen-Shannon divergence in each step of the search.