Information-theoretic lower bounds on the oracle complexity of sparse convex optimization
published: Jan. 13, 2011, recorded: December 2010, views: 4020
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Recent years have seen a surge in optimization methods tailored to sparse optimization problems. In this paper, we study the complexity of stochastic convex optimization in an oracle model of computation, when the objective is optimized at a sparse vector in a high dimensional space. Our result is matched by an appropriately tuned method of mirror descent, establishing the minimiax optimality of the result.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !