A Lower Bound for the Optimization of Finite Sums
published: Dec. 5, 2015, recorded: October 2015, views: 68
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.
This paper presents a lower bound for optimizing a finite sum of n functions, where each function is L-smooth and the sum is μ-strongly convex. We show that no algorithm can reach an error ϵ in minimizing all functions from this class in fewer than Ω(n+n(κ−1)−−−−−−−√log(1/ϵ)) iterations, where κ=L/μ is a surrogate condition number. We then compare this lower bound to upper bounds for recently developed methods specializing to this setting. When the functions involved in this sum are not arbitrary, but based on i.i.d. random data, then we further contrast these complexity results with those for optimal first-order methods to directly optimize the sum. The conclusion we draw is that a lot of caution is necessary for an accurate comparison, and identify machine learning scenarios where the new methods help computationally.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !