Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: We consider a multidimensional search problem that is motivated by questions in contextual decision-making, such as dynamic pricing and personalized medicine. Nature selects a state from a d-dimensional unit ball and then generates a sequence of d-dimensional directions. We are given access to the directions, but not access to the state. After receiving a direction, we have to guess the value of the dot product between the state and the direction. Our goal is to minimize the number of times when our guess is more than ǫ away from the true answer. We construct a polynomial time algorithm that we call Projected Volume achieving regret O(d log(d/ǫ)), which is optimal up to a log d factor. The algorithm combines a volume cutting strategy with a new geometric technique that we call cylindrification.

Multidimensional Binary Search for Contextual Decision-Making