Adaptive compressive measurements can offer significant system performance advantages due to online learning over non-adaptive or static compressive measurements for a variety of applications, such as image formation and target identification. However, such adaptive measurements tend to be sub-optimal due to their greedy design. Here, we propose a non-greedy adaptive compressive measurement design framework and analyze its performance for a face recognition task. While a greedy adaptive design aims to optimize the system performance on the next immediate measurement, a non-greedy adaptive design goes beyond that by strategically maximizing the system performance over all future measurements. Our non-greedy adaptive design pursues a joint optimization of measurement design and photon allocation within a rigorous information-theoretic framework. For a face recognition task, simulation studies demonstrate that the proposed non-greedy adaptive design achieves a nearly two to three fold lower probability of misclassification relative to the greedy adaptive and static designs. The simulation results are validated experimentally on a compressive optical imager testbed.