You are all cordially invited to the AMLab seminar on Tuesday May 16 at 16:00 in C3.163, where Tim van Erven (Leiden University) will give a talk titled “Multiple Learning Rates in Online Learning”. Afterwards there are the usual drinks and snacks!
In online convex optimization it is well known that certain subclasses of objective functions are much easier than arbitrary convex functions. We are interested in designing adaptive methods that can automatically get fast rates in as many such subclasses as possible, without any manual tuning. Previous adaptive methods are able to interpolate between strongly convex and general convex functions. We present a new method, MetaGrad, that adapts to a much broader class of functions, including exp-concave and strongly convex functions, but also various types of stochastic and non-stochastic functions without any curvature. For instance, MetaGrad can achieve logarithmic regret on the unregularized hinge loss, even though it has no curvature, if the data come from a favourable probability distribution. MetaGrad’s main feature is that it simultaneously considers multiple learning rates. Unlike all previous methods with provable regret guarantees, however, its learning rates are not monotonically decreasing over time and are not tuned based on a theoretically derived bound on the regret. Instead, they are weighted directly proportional to their empirical performance on the data using a tilted exponential weights master algorithm.
T. van Erven and W.M. Koolen. MetaGrad: Multiple Learning Rates in Online Learning. NIPS 2016.
W.M.Koolen, P. Grünwald and T. van Erven. Combining Adversarial Guarantees and Stochastic Fast Rates in Online Learning. NIPS 2016.