EE Seminar: On the Problem of On-Line Learning with Log-Loss

Speaker: Yaniv Fogel

M.Sc. student under the supervision of Prof. Meir Feder

Wednesday, January 3^th 2018 at 15:30

Room 011, Kitot Bldg., Faculty of Engineering

On the Problem of On-Line Learning with Log-Loss

Abstract

Broadly speaking, the task of inductive learning aims at utilizing past examples of data features and respective outcomes into a better prediction of the next outcome given its respective data sample.

In this talk we will consider the problem of on-line learning with respect to the logarithmic loss, where the learner provides a probability assignment for the next label given the past and current data features and the past labels.

Our first result is a class of new universal on-line probability assignment schemes based on the mixture approach.

Now, in classical learning, it is well known that there are model classes that can be learned in batch, but cannot be learned sequentially for adversarial data features and outcome sequences.

We show that for these model classes the proposed mixture schemes lead to a vanishing regret in the individual setting when the adversary is somewhat constrained.

In the stochastic setting we show that any on-line solution for the log-loss may be used to obtain a solution for a wide variety of loss functions.