  Deep learning models' architectures, including depth and width, are key
factors influencing models' performance, such as test accuracy and computation
time. This paper solves two problems: given computation time budget, choose an
architecture to maximize accuracy, and given accuracy requirement, choose an
architecture to minimize computation time. We convert this architecture
optimization into a subset selection problem. With accuracy's submodularity and
computation time's supermodularity, we propose efficient greedy optimization
algorithms. The experiments demonstrate our algorithm's ability to find more
accurate models or faster models. By analyzing architecture evolution with
growing time budget, we discuss relationships among accuracy, time and
architecture, and give suggestions on neural network architecture design.
