  In natural perception, different items (objects) in a scene are rarely
equally relevant to the observer. The brain improves performance by directing
attention to the most relevant items, for example the ones most likely to be
probed. For a general set of probing probabilities, it is not known how
attentional resources should be allocated to maximize performance. Here, we
investigate the optimal strategy for allocating a fixed resource budget E among
N items when on each trial, only one item gets probed. We develop an efficient
algorithm that, for any concave utility function, reduces the N-dimensional
problem to a set of N one-dimensional problems that the brain could plausibly
solve. We find that the intuitive strategy of allocating resource in proportion
to the probing probabilities is in general not optimal. In particular, in some
tasks, if resource is low, the optimal strategy involves allocating zero
resource to items with a nonzero probability of being probed. Our work opens
the door to normatively guided studies of attentional allocation.
