  Sequence optimization, where the items in a list are ordered to maximize some
reward has many applications such as web advertisement placement, search, and
control libraries in robotics. Previous work in sequence optimization produces
a static ordering that does not take any features of the item or context of the
problem into account. In this work, we propose a general approach to order the
items within the sequence based on the context (e.g., perceptual information,
environment description, and goals). We take a simple, efficient,
reduction-based approach where the choice and order of the items is established
by repeatedly learning simple classifiers or regressors for each "slot" in the
sequence. Our approach leverages recent work on submodular function
maximization to provide a formal regret reduction from submodular sequence
optimization to simple cost-sensitive prediction. We apply our contextual
sequence prediction algorithm to optimize control libraries and demonstrate
results on two robotics problems: manipulator trajectory prediction and mobile
robot path planning.
