Multidimensional Binary Search for Contextual Decision-Making

2 Nov 2016  ·  Ilan Lobel, Renato Paes Leme, Adrian Vladu ·

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 $\epsilon$ away from the true answer. We construct a polynomial time algorithm that we call Projected Volume achieving regret $O(d\log(d/\epsilon))$, 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.

PDF Abstract
No code implementations yet. Submit your code now


  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.


No methods listed for this paper. Add relevant methods here